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Suvodip Mukherjee

Publications and source records attributed to Suvodip Mukherjee.

At least 55 records · Page 3Linked to original sources

Multi-Tracer Correlated Stacking: A Novel Way to Discover Anisotropy in nano-Hz Stochastic Gravitational Wave Background

The isotropic stochastic gravitational wave background (SGWB) generated by a population of supermassive black hole binaries (SMBHBs) provides a unique window into their cosmic evolution. In addition to the isotropic power spectrum, the anisotropic component of the signal carries additional information about the supermassive black holes (SMBHs) and host galaxy connection. The measurement of this signal is usually carried out by angular power spectra, which is only a sufficient measure for a Gaussian and statistically isotropic distribution of SMBHBs, where the statistical properties of a field remain unchanged across the sky. In contrast, the contribution from SMBHBs in nano-hertz SGWB will be hosted by fewer massive galaxies, making the nano-hertz background anisotropic and non-Gaussian. As a result, the performance of angular power spectra in extracting the underlying physics is limited. In this work, we propose a novel technique called the \texttt{Multi-Tracer Correlated Stacking}, which enables the detection of anisotropies in the SGWB by stacking the signal from regions of the sky with tracers of BHs such as active galactic nucleus (AGNs), quasars, bright galaxies, etc., that can be mapped up to high redshift. We demonstrate this technique on a simulated supermassive BHBs distribution using an AGN catalog, which maps the underlying matter distribution approximately up to redshift $z=5$. This stacking technique uniquely distinguishes between isotropic and anisotropic distributions of SGWB source, surpassing the capabilities of angular power spectrum-based methods in detecting anisotropic signals. This highlights the effectiveness of this technique in detecting anisotropic SGWB signals and in the future, this technique can play a crucial role in its discovery.

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SpectrAx: Spectral Search of Axion-Like Particles Using Multi-Band Observations of Galaxy Clusters from SKA, SO, CMB-S4 and eROSITA

The existence of axions or Axion-Like Particles (ALPs) has been predicted by various Beyond Standard Model (BSM) theories, and the proposed photon-ALP interaction is one of the ways to probe them. Such an interaction will lead to photon-ALP resonant conversion in galaxy clusters, resulting in a polarized spectral distortion in the CMB along the cluster line of sight. The estimation of this signal from galaxy clusters requires an estimation of their electron density and magnetic field profiles, as well as their redshifts. We have developed a new Bayesian framework \texttt{SpectrAx} that can use observations from different electromagnetic bands such as radio, CMB, optical, and X-ray to infer the astrophysical properties of a galaxy cluster, such as cluster its redshift, electron density and magnetic field, along with the BSM physics such as ALPs. We use simulated redshifts in our analysis, but that can be obtained by cross-matching with optical surveys having overlapping sky regions with the galaxy clusters. Also, we use radial profiles that are motivated from observations of galaxy clusters at low redshifts. By using the simulated data corresponding to the ALP mass of $10^{-14}$ eV for upcoming CMB surveys such as Simons Observatory (SO) and CMB-S4 in combination with Square Kilometer Array (SKA) and extended ROentgen Survey with an Imaging Telescope Array (eROSITA) we demonstrate the capability in accurately inferring the ALPs coupling strength along with the radial profile of electron density and magnetic field from galaxy clusters. The application of this framework to the data from future surveys by combining SKA+SO+eROSITA and SKA+CMB-S4+eROSITA will make it possible for the first time to explore both astrophysics and BSM physics from low-redshift galaxy clusters using a multi-band approach.

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Multi-Messenger Cosmology: A Route to Accurate Inference of Dark Energy Beyond CPL Parametrization from XG Detectors

One of the central challenges in modern cosmology is understanding the nature of dark energy and its evolution throughout the history of the Universe. Dark energy is commonly modeled as a perfect fluid with a time-varying equation-of-state parameter, $w(z)$, often modeled under CPL parametrization using two parameters $w_0$ and $w_a$. In this study, we explore both parametric and non-parametric methods to reconstruct the dark energy Equation of State (EoS) using Gravitational Wave (GW) sources, with and without electromagnetic (EM) counterparts called bright sirens and dark sirens respectively. In the parametric approach, we extend the widely used $w_0$-$w_a$ model by introducing an additional term, $w_b$, to better capture the evolving dynamics of dark energy up to high redshift which is accessible from GW sources. This extension provides increased flexibility in modeling the EoS and enables a more detailed investigation of dark energy's evolution. Our analysis indicates that, with five years of observation time and a $75\%$ duty cycle using Cosmic Explorer and the Einstein Telescope, it will be possible to measure the dark energy EoS with remarkable precision, better than any other cosmological probe in the coming years, from bright standard sirens using a multi-messenger approach. These findings highlight the potential of GW observations in synergy with EM telescopes to offer valuable insights into the nature of dark energy, overcoming the current limitations in cosmological measurements.

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Accelerated parameter estimation of supermassive black hole binaries in LISA using a meshfree approximation

The Laser Interferometer Space Antenna (LISA) will be capable of detecting gravitational waves (GWs) in the milli-Hertz band. Among various sources, LISA will detect the coalescence of supermassive black hole binaries (SMBHBs). Accurate and rapid inference of parameters for such sources will be important for potential electromagnetic follow-up efforts. Rapid Bayesian inference with LISA includes additional complexities as compared to current generation terrestrial detectors in terms of time and frequency dependent antenna response functions. In this work, we extend a recently developed, computationally efficient technique that uses meshfree interpolation methods to accelerate Bayesian reconstruction of compact binaries. Originally developed for second-generation terrestrial detectors, this technique is now adapted for LISA parameter estimation. Using the full inspiral, merger, and ringdown waveform (PhenomD) and assuming rigid adiabatic antenna response function, we show faithful inference of SMBHB parameters from GW signals embedded in stationary, Gaussian instrumental noise. We discuss the computational cost and performance of the meshfree approximation method in estimating the GW source parameters.

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The Lunar Gravitational-wave Antenna: Mission Studies and Science Case

The Lunar Gravitational-wave Antenna (LGWA) is a proposed array of next-generation inertial sensors to monitor the response of the Moon to gravitational waves (GWs). Given the size of the Moon and the expected noise produced by the lunar seismic background, the LGWA would be able to observe GWs from about 1 mHz to 1 Hz. This would make the LGWA the missing link between space-borne detectors like LISA with peak sensitivities around a few millihertz and proposed future terrestrial detectors like Einstein Telescope or Cosmic Explorer. In this article, we provide a first comprehensive analysis of the LGWA science case including its multi-messenger aspects and lunar science with LGWA data. We also describe the scientific analyses of the Moon required to plan the LGWA mission.

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Detecting Unmodeled, Source-dependent Signals in Gravitational Waves with SCoRe

New physics and systematic errors can lead to deviations between the models used to analyze gravitational wave data and the actual signal. Such deviations will generally be correlated between detectors and manifest differently across the gravitational wave source parameter space. The previously introduced \ttt{SCoRe} framework uses these features to distinguish these deviations from noise and extract physical information from their source-dependent variation. In this work, we further analyze the hierarchical component of the method -- we include the expected dependence of the deviations on the source parameters into the inference process, obtaining more physically informative results. As a specific example, we study a deviation that scales as a power law of the mass scale of black hole binaries -- as, for example, in Effective Field Theory of gravity. We show how the signal-to-noise ratio of the cross-correlated residual power can be used to recover the power-law index. We demonstrate how both the distribution in source and deviation strength determine which region of source parameter space influences the inference most. Finally, we forecast the constraint on the power law index for a network of two Cosmic Explorer-like detectors with a year of observation period.

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Be careful in multi-messenger inference of the Hubble constant: A path forward for robust inference

Multi-messenger observations of coalescing binary neutron stars (BNSs) are a direct probe of the expansion history of the universe and carry the potential to shed light on the disparity between low- and high-redshift measurements of the Hubble constant $H_0$. To measure the value of $H_0$ with such observations requires pristine inference of the luminosity distance and the true source redshift with minimal impact from systematics. In this analysis, we carry out joint inference on mock gravitational wave (GW) signals and their electromagnetic (EM) afterglows from BNS coalescences and find that the inclination angle inferred from the afterglow light curve and apparent superluminal motion can be precise, but need not be accurate and is subject to systematic uncertainty that could be as large as $1.5σ$. This produces a disparity between the EM and GW inferred inclination angles, which if not carefully treated when combining observations can bias the inferred value of $H_0$. We also find that already small misalignments of $3^{\circ}-6^{\circ}$ between the inherent system inclinations for the GW and EM emission can bias the inference by $\mathcal{O}(1-2σ)$ if not taken into account. As multi-messenger BNS observations are rare, we must make the most out of a small number of events and harness the increased precision, while avoiding reduced accuracy. We demonstrate how to mitigate these potential sources of bias by jointly inferring the mismatch between the GW- and EM-based inclination angles and $H_0$.

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A Model-Independent Precision Test of General Relativity using LISA Bright Standard Sirens

The upcoming Laser Interferometer Space Antenna (LISA), set for launch in the mid-2030s, will enhance our capability to probe the universe through gravitational waves (GWs) emitted from binary black holes (BBHs) across a broad range of cosmological distances. LISA is projected to observe three classes of BBHs: massive BBHs (MBBHs), extreme mass-ratio inspirals (EMRIs), and stellar mass BBHs. This study focuses on MBBHs, which are anticipated to occur in gas-rich environments conducive to producing powerful electromagnetic (EM) counterparts, positioning them as excellent candidates for bright sirens. By combining GW luminosity distance measurements from these bright sirens with Baryon Acoustic Oscillation (BAO) measurements derived from galaxy clustering and sound horizon measurements from the Cosmic Microwave Background (CMB), and spectroscopic redshift measurements from electromagnetic (EM) observations, we propose a data-driven model-independent method to reconstruct deviations in the variation of the effective Planck mass (in conjunction with the Hubble constant) as a function of cosmic redshift. Using this multi-messenger technique, we achieve precise measurements of deviations in the effective Planck mass variation with redshift (z), with a precision ranging from approximately $2.4\%$ to $7.2\%$ from redshift $z=1$ to $z=6$ with a single event. Additionally, we achieved a measurement of the Hubble constant with a precision of about $1.3\%$, accounting for variations in the effective Planck mass over 4 years of observation time ($T_{\mathrm{obs}}$). This assumes that EM counterparts are detected for $75\%$ of the events. This precision improves with observation time as $T_{\mathrm{obs}}^{-1/2}$. This approach not only has the potential to reveal deviations from General Relativity but also to significantly expand our understanding of the universe's fundamental physical properties.

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Dual AGNs: Precursors of Binary Supermassive Black Hole Formation and Mergers

The presence of dual active galactic nuclei (AGN) on scales of a few tens of kpc can be used to study merger-induced accretion on supermassive black holes (SMBHs) and offer insights about SMBH mergers, using dual AGNs as merger precursors. This study uses the {\sc Romulus25} cosmological simulation to investigate the properties and evolution of dual AGNs. We first analyze the properties of AGNs ($L_{bol} > 10^{43} \rm $ erg s$^{-1}$) and their neighboring SMBHs (any SMBHs closer than 30 pkpc to an AGN) at $z \leq 2$. This is our underlying population. We then applied the luminosity threshold of $L_{bol} > 10^{43} $ erg s$^{-1}$ to the neighboring SMBHs thereby identifying dual and multiple AGNs. Our findings indicate an increase in the number of both single and dual AGNs from lower to higher redshifts. We also find that the number of dual AGNs with separations of 0.5-4 kpc is twice the number of duals with separations of 4-30 kpc. All dual AGNs in our sample resulted from major mergers. Compared to single AGNs, duals have a lower black hole-to-halo mass ratio. We found that the properties of dual AGN host halos, including halo mass, stellar mass, star formation rate (SFR), and gas mass, are generally consistent with those of single AGN halos, albeit tending towards the higher end of their respective property ranges. Our analysis uncovered a diverse array of evolutionary patterns among dual AGNs, including rapidly evolving systems, slower ones, and instances where SMBH mergers are ineffective.

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Cross-correlating dark sirens and galaxies: constraints on $H_0$ from GWTC-3 of LIGO-Virgo-KAGRA

We apply the cross-correlation technique to infer the Hubble constant ($H_0$) of the Universe using gravitational wave (GW) sources without electromagnetic counterparts (dark sirens) from the third GW Transient Catalog (GWTC-3) and the photometric galaxy surveys 2MPZ and WISE-SuperCOSMOS, and combine these with the bright siren measurement of $H_0$ from GW170817. The posterior on $H_0$ with only dark sirens is uninformative due to the small number of well-localised GW sources. Using the eight well-localized dark sirens and the binary neutron star GW170817 with EM counterpart, we obtain a value of the Hubble constant $H_0= 75.4_{-6}^{+11}$ km/s/Mpc (median and 68.3$\%$ equal-tailed interval (ETI)) after marginalizing over the matter density and the GW bias parameters. This measurement is mostly driven by the bright siren measurement and any constraint from dark sirens is not statistically significant. In the future, with more well-localized GW events, the constraints on expansion history will improve.

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A power spectrum approach to the search for Axion-like Particles from resolved galaxy clusters using CMB as a backlight

Axions or ALPs are hypothetical particles predicted by BSM theories, which make one of the dark matter candidates. These particles can convert into photons and vice-versa in the presence of magnetic field, with a probability decided by its coupling strength $\mathrm{g_{aγ}}$. One of the ways to detect these particles is using the CMB as a backlight. As the CMB photons pass through a galaxy cluster, they can get converted into ALPs in the mass range $10^{-15}$ eV to $10^{-11}$ eV through resonant conversion in the presence of cluster magnetic fields. This leads to a polarized spectral distortion ($α$-distortion) in the CMB as the photon polarization parallel to the magnetic field in the galaxy cluster is involved in the conversion. The fluctuations in the magnetic field and electron density in a galaxy cluster lead to spatially varying $α$-distortion around the cluster, with a power spectrum that is different from the lensed CMB polarization power spectrum for the standard model of cosmology. By measuring the difference in the polarization power spectrum around a galaxy cluster from the all-sky signal, one can find new $α$-distortion in the sky. For galaxy clusters resolvable in multiple EM bands, one can measure the coupling strength $\mathrm{g_{aγ}}$ from the ALP power spectrum. Using multi-frequency techniques like ILC to clean the foregrounds, we show that the new power spectrum-based approach of the resolved galaxy clusters from upcoming CMB experiments such as Simons Observatory and CMB-S4 can detect (or put constraints) on the ALP-photon coupling strength of $\mathrm{g_{aγ} < 5.2 \times 10^{-12} \, GeV^{-1}}$ and $\mathrm{g_{aγ} < 3.6 \times 10^{-12} \, GeV^{-1}}$ at 95\% C.I. respectively for ALPs of masses $10^{-13}$ eV or for smaller $\mathrm{g_{aγ}}$ for lighter ALP masses (Abridged).

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Prospect of Precision Cosmology and Testing General Relativity using Binary Black Holes- Galaxies Cross-correlation

Modified theories of gravity predict deviations from General Relativity (GR) in the propagation of gravitational waves (GW) across cosmological distances. A key prediction is that the GW luminosity distance will vary with redshift, differing from the electromagnetic (EM) luminosity distance due to varying effective Planck mass. We introduce a model-independent, data-driven approach to explore these deviations using multi-messenger observations of dark standard sirens (Binary Black Holes, BBH). By combining GW luminosity distance measurements from dark sirens with Baryon Acoustic Oscillation (BAO) measurements, BBH redshifts inferred from cross-correlation with spectroscopic or photometric galaxy surveys, and sound horizon measurements from the Cosmic Microwave Background (CMB), we can make a data-driven test of GR (jointly with the Hubble constant) as a function of redshift. Using the multi-messenger technique with the spectroscopic DESI galaxy survey, we achieve precise measurements of deviations in the effective Planck mass variation with redshift. For the Cosmic Explorer and Einstein Telescope (CEET), the best precision is approximately 3.6\%, and for LIGO-Virgo-KAGRA (LVK), it is 7.4\% at a redshift of $\rm{z = 0.425}$. Additionally, we can measure the Hubble constant with a precision of about 1.1\% from CEET and 7\% from LVK over five years of observation with a 75\% duty cycle. We also explore the potential of cross-correlation with photometric galaxy surveys from the Rubin Observatory, extending measurements up to a redshift of $\rm{z \sim 2.5}$. This approach can reveal potential deviations from models affecting GW propagation using numerous dark standard sirens in synergy with DESI and the Rubin Observatory.

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GLANCE -- Gravitational Lensing Authenticator using Non-Modelled Cross-Correlation Exploration of Gravitational Wave Signals

Gravitational lensing is the phenomenon where the presence of matter (called a lens) bends the path of light-like trajectories travelling nearby. Similar to the geometric optics limit of electromagnetic waves, gravitational lensing of gravitational waves (GWs) can occur in geometric optics condition when GW wavelength is much smaller than the Schwarzschild radius of the lens i.e. $λ_{GW} \ll$ R$^{\rm s}_{\rm lens}$. This is known as the strong-lensing regime for which a multiple-image system with different magnifications and phase-shifts is formed. We developed $\texttt{GLANCE}$, Gravitational Lensing Authenticator using Non-modelled Cross-correlation Exploration, a novel technique to detect strongly lensed GW signals. We demonstrate that cross-correlation between two noisy reconstruction of polarized GW signals shows a non-zero value when the signals are lensed counterparts. The relative strength between the signal cross-correlation and noise cross-correlation can quantify the significance of the event(s) being lensed. Since lensing biases the inference of source parameters, primarily the luminosity distance, a joint parameter estimation of the source and lens-induced parameters is incorporated using a Bayesian framework. We applied $\texttt{GLANCE}$ to synthetic strong lensing data and showed that it can detect lensed GW signals and correctly constrain the injected source and lens parameters, even when one of the signals is below match-filtered threshold signal-to-noise ratio. This demonstrates $\texttt{GLANCE}'$s capability as a robust detection technique for strongly lensed GW signals and can distinguish between lensed and unlensed events.

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Imprints of Supermassive Black Hole Evolution on the Spectral and Spatial Anisotropy of Nano-Hertz Stochastic Gravitational-Wave Background

The formation and evolution of supermassive black holes (SMBHs) remains an open question in the field of modern cosmology. The detection of nanohertz (n-Hz) gravitational waves via pulsar timing arrays (PTAs) in the form of individual events and the stochastic gravitational wave background (SGWB) offers a promising avenue for studying SMBH evolution across cosmic time, with SGWB signal being the immediately detectable signal with the currently accessible telescope sensitivities. By connecting the galaxy properties in the large scale (Gpc scale) cosmological simulation such as \texttt{MICECAT} with the small scale ($\sim$ Mpc scale) galaxy simulations from \texttt{ROMULUS}, we show that different scenarios of galaxy-SMBH evolution with redshift leads to a frequency-dependent spatial anisotropy in the SGWB signal. The presence of slow evolution of the SMBHs in the Universe leads to a pronounced blue anisotropic spectrum of the SGWB. In contrast, if SMBHs grow faster in the Universe in lighter galaxies, the frequency-dependent spatial anisotropy exhibits a more flattened anisotropic spectrum. This additional aspect of the SGWB signal on top of the monopole SGWB signal, can give insight on how the SMBHs form in the high redshift Universe and its interplay with the galaxy formation from future measurements.

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A Diffused Background from Axion-like Particles in the Microwave Sky

The nature of dark matter is an unsolved cosmological problem and axions are one of the weakly interacting cold dark matter candidates. Axions or ALPs (Axion-like particles) are pseudo-scalar bosons predicted by beyond-standard model theories. The weak coupling of ALPs with photons leads to the conversion of CMB photons to ALPs in the presence of a transverse magnetic field. If they have the same mass as the effective mass of a photon in a plasma, the resonant conversion would cause a polarized spectral distortion leading to temperature fluctuations with the distortion spectrum. The probability of resonant conversion depends on the properties of the cluster such as the magnetic field, electron density, and its redshift. We show that this kind of conversion can happen in numerous unresolved galaxy clusters up to high redshifts, which will lead to a diffused polarised anisotropy signal in the microwave sky. The spectrum of the signal and its shape in the angular scale will be different from the lensed CMB polarization signal. This new polarised distortion spectrum will be correlated with the distribution of clusters in the universe and hence, with the large-scale structure. The spectrum can then be probed using its spectral and spatial variation with respect to the CMB and various foregrounds. An SNR of $\sim$ 4.36 and $\sim$ 93.87 are possible in the CMB-S4 145 GHz band and CMB-HD 150 GHz band respectively for a photon-ALPs coupling strength of $\mathrm{g_{a γ} = 10^{-12} \, GeV^{-1}}$ using galaxy clusters beyond redshift z $= 1$. The same signal would lead to additional RMS fluctuations of $\sim \mathrm{7.5 \times 10^{-2} \, μK}$ at 145 GHz. In the absence of any signal, future CMB experiments such as Simons Observatory (SO), CMB-S4, and CMB-HD can put constraints on coupling strength better than current bounds from particle physics experiment CERN Axion Solar Telescope (CAST).

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Discovering the Cosmic Evolution of Supermassive Black Holes using Nano-Hertz Gravitational Waves and Galaxy Surveys

The formation and evolution of supermassive black holes (SMBHs) in the Universe remains an open question in cosmology. We show for the first time that the evolution of SMBHs with redshift leads to a unique signature on the angular cross-correlation power spectrum between the multi-frequency nano-hertz (nHz) stochastic gravitational wave (SGWB) and the galaxy density in the Universe. By using galaxy catalogs from the upcoming Rubin LSST Observatory in synergy with the nHz SGWB signal accessible from the Square Kilometer Array, we can measure this signal with a signal-to-noise ratio above five, thereby opening a new observational window to the cosmic evolution of SMBHs across redshift. This discovery space that can be opened by the cross-correlation of the nHz SGWB will not be possible by any other currently known techniques.

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A Model-Independent Precision Test of General Relativity using Bright Standard Sirens from ongoing and upcoming detectors

Gravitational waves (GWs) provide a new avenue to test Einstein's General Relativity (GR) using the ongoing and upcoming GW detectors by measuring the redshift evolution of the effective Planck mass proposed by several modified theories of gravity. We propose a model-independent, data-driven approach to measure any deviation from GR in the GW propagation effect by combining multi-messenger observations of GW sources accompanied by EM counterparts, commonly known as bright sirens (Binary Neutron Star (BNS) and Neutron Star Black Hole systems (NSBH)). We show that by combining the GW luminosity distance measurements from bright sirens with the Baryon Acoustic Oscillation (BAO) measurements derived from galaxy clustering, and the sound horizon measurements from the Cosmic Microwave Background (CMB), we can make a data-driven reconstruction of deviation of the variation of the effective Planck mass (jointly with the Hubble constant) as a function of cosmic redshift. Using this technique, we achieve a precise measurement of GR with redshift (z) with a precision of approximately $7.9\%$ for BNSs at redshift z=0.075 and $10\%$ for NSBHs at redshift z=0.225 with 5 years of observation from LIGO-Virgo-KAGRA network of detectors. Employing Cosmic Explorer and Einstein Telescope for just 1 year yields the best precision of about $1.62\%$ for BNSs and $2\%$ for NSBHs at redshift z=0.5 on the evolution of the frictional term, and a similar precision up to z=1. This measurement can discover potential deviation from any kind of model that impacts GW propagation with ongoing and upcoming observations.

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Probing the Physics of Reionization Using kSZ Power Spectrum from Current and Upcoming CMB Surveys

The patchiness in the reionization process alters the statistics of Cosmic Microwave Background (CMB), with the kinematic Sunyaev-Zeldovich (kSZ) effect in the CMB temperature power spectrum being a notable consequence. In this work, we aim to explore the potential of future kSZ power spectrum measurements in inferring the details of the reionization process. In this pursuit, we capitalize on the recent developments in foreground mitigation techniques using the Cross-Internal Linear Combination (Cross-ILC) technique, which enables robust detection of the kSZ power spectrum with signal-to-noise ($S/N$) roughly $20-30σ$ in this decade by SPT-3G and Simons Observatory (SO); and $\geq 80σ$ by CMB-S4, substantially improving on the recent evidence for kSZ binned at $\ell=3000$ using SPT-SZ+SPTpol surveys. We use a fiducial kSZ power spectrum along with realistic error bars expected from the above technique for SPT-3G, SO, and CMB-S4 to constrain the parameter space for a physical model of reionization. We find that with the improved error bars it will be possible to place stringent constraints on reionization using solely the Cross-ILC recovered SPT-3G kSZ without imposing any prior on $τ$ in the Bayesian inference. Notably, high-fidelity kSZ measurements from CMB-S4 coupled with $τ$ measurements through LiteBIRD will enable unprecedented constraint on the midpoint of reionization with an error bar of $\sim 0.25$ and the duration of reionization with an error bar at $\sim 0.21$ exclusively using CMB data. This study highlights the need to capture kSZ power spectrum on a broad range of multipoles to gain insights into the inhomogeneous reionization era.

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