arXiv subjects

Akshay Rana

Publications and source records attributed to Akshay Rana.

10 recordsLinked to original sources

arXiv2025

Spectral Chebyshev Approximation of Cosmic Expansion in $f(R)$ Gravity

We present a numerical framework to study the cosmological background evolution in $f(R)$ gravity by employing a \textit{spectral Chebyshev collocation approach}. Unlike standard integration methods such as Runge--Kutta that often encounter stiffness and accuracy issues, this formulation expands the normalized Hubble function $E(z) = H(z)/H_0$ as a finite Chebyshev series. The modified Friedmann equation is then enforced at selected Chebyshev--Gauss--Lobatto points, converting the original nonlinear differential equation into a system of algebraic relations for the series coefficients. This transformation yields exponentially convergent and numerically stable solutions over the entire redshift domain, $0<z<z_{max}$, eliminating the need for adaptive step-size control. We apply the method to two widely studied $f(R)$ models, Hu--Sawicki and Starobinsky, and perform a combined analysis using cosmic chronometer $H(z)$ data and the Union~3.0 supernova compilation. The reconstructed expansion histories match observations to within $2\sigma$ over $0 < z < 2$, producing best-fit parameters of approximately $(\Omega_{m0}, H_0, \Lambda_{\mathrm{eff}}) \simeq (0.29, 68, 1.2\text{--}2.5\,H_0^2)$. These results indicates that both models reproduce the observed late-time acceleration while permitting small geometric corrections to $\Lambda$CDM. Overall, the spectral Chebyshev method provides a precise and computationally efficient framework for probing modified-gravity cosmologies in the precision-data era.

astro-ph.CO↗

arXiv2025

Testing the Constancy of Type Ia Supernova Luminosities with Gaussian Process

Type Ia supernovae (SNe~Ia) are central to studies of cosmic expansion, under the assumption that their absolute magnitude $M_B$ does not evolve with redshift. Even small drifts in brightness can bias cosmological parameters such as $H_0$ and $w$. Here we test this assumption using a non-parametric Gaussian Process (GP) reconstruction of the expansion history from cosmic chronometer $H(z)$ data, which provides a model-independent baseline distance modulus, $\mu_{\rm GP}(z)$. To propagate uncertainties, we draw Monte Carlo realizations of $H(z)$ from the GP posterior and evaluate them on a Chebyshev grid, which improves numerical stability and quadrature accuracy. Supernova observations are then compared to this baseline through residuals, $\Delta M_B(z)$, and their derivatives. Applying this method to Pantheon+ (1701 SNe~Ia) and DES 5YR (435 SNe~Ia), we find that SNe~Ia are consistent with being standard candles within $1\sigma$, though both datasets exhibit localized departures: near $z \sim 1$ in Pantheon+ and at $z \sim 0.3$--$0.5$ in DES. The presence of similar features in two independent surveys suggests they are not purely statistical. Our results point toward a possible non-monotonic luminosity evolution, likely reflecting different physical drivers at different epochs, and highlight the need for a deeper astrophysical understanding of SN~Ia populations.

astro-ph.CO↗

arXiv2023

Constraints on the Transition Redshift using Hubble Phase Space Portrait

One of the most significant discoveries in modern cosmology is that the universe is currently in a phase of accelerated expansion after a switch from a decelerated expansion. The redshift corresponding to this epoch is referred to as the transition redshift $z_t$. In this work we put constraints on the $z_t$ with both model-independent and model-dependent approaches. We consider 32 Hubble parameter measurements and the Pantheon sample of Type Ia Supernovae (SNe). In order to include the possible systematic effects in this analysis, we use the full covariance matrix of systematic uncertainties for the Hubble parameter measurements. We plot a Hubble Phase Space Portrait (HPSP) between $\dot{H}(z)$ and $H(z)$ in a model-independent way. From this HPSP diagram, we estimate the transition redshift as well as the current value of the equation of state parameter $ω_0$ in a model-independent way. By considering H(z) measurements, we find the best fit value of $z_t=0.591^{+0.332}_{-0.332}$ and $ω_0=-0.677^{+0.238}_{-0.238}$. We obtain the best fit value of $z_t=0.849^{+0.117}_{-0.117}$ and $ω_0=-0.870^{+0.013}_{-0.013}$ using the Pantheon database. Further, we also use a model dependent approach to determine $z_t$. Here, we consider a non-flat $Λ$CDM model as a background cosmological model. We reconstruct the cosmic triangle plot among $\log(Ω_{m0})$, $-\log(2Ω_{\Lambda0})$ and $3\log(1+z_t)$ where the constraints of each parameter are determined by the location in this triangle plot. Using $Ω_{m0}$ and $Ω_{\Lambda0}$ values, we find the best value of the transition redshift $z_t=0.619^{+0.580}_{-0.758}$, which is in good agreement with the Planck 2018 results at $1σ$ confidence level. We also simulate the observed Hubble parameter measurements in the redshift range $0<z<2$ and perform the same analysis to estimate the transition redshift.

astro-ph.CO↗

arXiv2023

Examining Temporal Variation of the Fermi Coupling Constant using SNe Ia Light Curves

In standard model, the Fermi coupling constant, $G_F$, sets the strength of electroweak decay. We attempt an approach to constrain the temporal variation of the Fermi coupling constant $G_F$. To probe it, Type Ia supernovae (SNe Ia) light curves are being used as a source of reliable primordial nucleosynthesis events across the redshifts. We utilized studies suggesting that in the initial phase after the SNe Ia explosion, the electroweak decay of $^{56}Ni \rightarrow ^{56}Co \rightarrow ^{56}Fe$ is the key contributor to powering the SNe Ia light curve. We hence used the Pan-STARRS supernovae catalog having 1169 supernovae light curves in $g$, $r$, $i$, and $z$ spectral filters. The post-peak decrease in the apparent magnitude of light curves (in the rest frame of SNe) was related to the electroweak decay rate of primordial nucleosynthesis. Further, the decay rate relates to $G_F$. To keep the analysis independent of the cosmological model, we used the Hubble parameter measurement and a non-parametric statistical method, the Gaussian Process. Our study suggests a small yet finite temporal variation of $G_F$ and puts a strong upper bound on the present value of the fractional change in the Fermi coupling constant i.e; $\dfrac{\dot G_F}{G_F}\big\rvert_{z=0} \approx 10^{-11} yr^{-1}$ using datasets spread over a redshift range $0<z<0.75$.

astro-ph.CO↗

arXiv2022

A non-parametric test of variability of Type Ia supernovae luminosity and CDDR

The first observational evidence for cosmic acceleration appeared from Type Ia supernovae (SNe Type Ia) Hubble diagram from two different groups. However, the empirical treatment of SNe Type Ia and their ability to show cosmic acceleration have been the subject of some debate in the literature. In this work we probe the assumption of redshift-independent absolute magnitude $(M_{\mathrm{B}})$ of SNe along with its correlation with spatial curvature ($Ω_{k0}$) and cosmic distance duality relation (CDDR) parameter ($η(z)$). This work is divided into two parts. Firstly, we check the validity of CDDR which relates the luminosity distance ($d_L$) and angular diameter distance ($d_A$) via redshift. We use the Pantheon SNe Ia dataset combined with the $H(z)$ measurements derived from the cosmic chronometers. Further, four different redshift-dependent parametrizations of the distance duality parameter $(η(z))$ are used. The CDDR is fairly consistent for almost every parametrization within a $2σ$ confidence level in both flat and a non-flat universe. In the second part, we assume the validity of CDDR and emphasize on the variability of $M_{\mathrm{B}}$ and its correlation with $Ω_{k0}$. We choose four different redshift-dependent parametrizations of $M_{\mathrm{B}}$. The results indicate no evolution of $M_{\mathrm{B}}$ within $2σ$ confidence level. For all parametrizations, the best fit value of $Ω_{k0}$ indicates a flat universe at $2σ$ confidence level. However a mild inclination towards a non flat universe is also observed. We have also examined the dependence of the results on the choice of different priors for $H_0$.

astro-ph.CO↗

arXiv2022

Strong lensing systems and galaxy cluster observations as probe to the cosmic distance duality relation

{In this paper, we use large scale structure observations to test the redshift dependence of cosmic distance duality relation (CDDR), $D_{\rm L}(1+z)^{-2}/D_{\rm A}=η(z)$}, with $D_{\rm L}$ and $D_{\rm A}$, being the luminosity and angular diameter distances, respectively. In order to perform the test, the following data set are considered: strong lensing systems and galaxy cluster measurements (gas mass fractions). No specific cosmological model is adopted, only a flat universe is assumed. { By considering two $η(z)$ parametrizations, It is observed that the CDDR remain redshift independent within $1.5σ$ which is in full agreement with other recent tests involving cosmological data}. It is worth to comment that our results are independent of the baryon budget of galaxy clusters.

astro-ph.CO↗

arXiv2018

Bounds on graviton mass using weak lensing and SZ effect in galaxy clusters

In General Relativity (GR), the graviton is massless. However, a common feature in several theoretical alternatives of GR is a non-zero mass for the graviton. These theories can be described as massive gravity theories. Despite many theoretical complexities in these theories, on phenomenological grounds, the implications of massive gravity have been widely used to put bounds on graviton mass. One of the generic implications of giving a mass to the graviton is that the gravitational potential will follow a Yukawa-like fall off. We use this feature of massive gravity theories to probe the mass of graviton by using the largest gravitationally bound objects, namely galaxy clusters. In this work, we use the mass estimates of galaxy clusters measured at various cosmologically defined radial distances measured via weak lensing (WL) and Sunyaev-Zel'dovich (SZ) effect. We also use the model independent values of Hubble parameter $H(z)$ smoothed by a non-parametric method, Gaussian process. Within $1σ$ confidence region, we obtain the mass of graviton $m_g < 5.9 \times 10^{-30}$ eV with the corresponding Compton length scale $λ_g > 6.82$ Mpc from weak lensing and $m_g < 8.31 \times 10^{-30}$ eV with $λ_g > 5.012$ Mpc from SZ effect. This analysis improves the upper bound on graviton mass obtained earlier from galaxy clusters.

astro-ph.CO↗

arXiv2017

Probing the cosmic distance duality relation using time delay lenses

The construction of the cosmic distance-duality relation (CDDR) has been widely studied. However, its consistency with various new observables remains a topic of interest. We present a new way to constrain the CDDR $η(z)$ using different dynamic and geometric properties of strong gravitational lenses (SGL) along with SNe Ia observations. We use a sample of $102$ SGL with the measurement of corresponding velocity dispersion $σ_0$ and Einstein radius $θ_E$. In addition, we also use a dataset of $12$ two image lensing systems containing the measure of time delay $Δt$ between source images. Jointly these two datasets give us the angular diameter distance $D_{A_{ol}}$ of the lens. Further, for luminosity distance, we use the $740$ observations from JLA compilation of SNe Ia. To study the combined behavior of these datasets we use a model independent method, Gaussian Process (GP). We also check the efficiency of GP by applying it on simulated datasets, which are generated in a phenomenological way by using realistic cosmological error bars. Finally, we conclude that the combined bounds from the SGL and SNe Ia observation do not favor any deviation of CDDR and are in concordance with the standard value ($η=1$) within $2σ$ confidence region, which further strengthens the theoretical acceptance of CDDR.

astro-ph.CO↗

arXiv2017

Constraining cosmic curvature by using age of galaxies and gravitational lenses

We use two model-independent methods to constrain the curvature of the universe. In the first method, we study the evolution of the curvature parameter ($Ω_k^0$) with redshift by using the observations of the Hubble parameter and transverse comoving distances obtained from the age of galaxies. Secondly, we also use an indirect method based on the mean image separation statistics of gravitationally lensed quasars. The basis of this methodology is that the average image separation of lensed images will show a positive, negative or zero correlation with the source redshift in a closed, open or flat universe respectively. In order to smoothen the datasets used in both the methods, we use a non-parametric method namely, Gaussian Process (GP). Finally from first method we obtain $Ω_k^0= 0.025\pm0.57$ for a presumed flat universe while the cosmic curvature remains constant throughout the redshift region $0<z<1.37$ which indicates that the universe may be homogeneous. Moreover, the combined result from both the methods suggests that the universe is marginally closed. However, a flat universe can be incorporated at $3σ$ level.

astro-ph.CO↗

arXiv2016

Revisiting the distance duality relation using a non-parametric regression method

The interdependence of luminosity distance, $D_L$ and angular diameter distance, $D_A$ given by the distance duality relation (DDR) is very significant in observational cosmology. It is very closely tied with the temperature- redshift relation of Cosmic Microwave Background (CMB) radiation. Any deviation from $η(z)\equiv \frac{D_L}{D_A (1+z)^2} =1$ indicates a possible emergence of new physics. Our aim in this work is to check the consistency of these relations using a non-parametric regression method namely, LOESS with SIMEX. This technique avoids dependency on the cosmological model and works with a minimal set of assumptions. Further, to analyze the efficiency of the methodology, we simulate a dataset of $200$ points of $η(z)$ data based on a phenomenological model $η(z)= (1+z)^ε$. The error on the simulated data points is obtained by using the temperature of CMB radiation at various redshifts. For testing the distance duality relation, we use the JLA SNe Ia data for luminosity distances, while the angular diameter distances are obtained from radio galaxies datasets. Since the DDR is linked with CMB temperature - redshift relation, therefore we also use the CMB temperature data to reconstruct $η(z)$. It is important to note that with CMB data, we are able to study the evolution of DDR up to a very high redshift $ z = 2.418$. In this analysis, we find no evidence of deviation from $η=1$ within a $1σ$ region in the entire redshift range used in this analysis ($0 < z \leq 2.418$).

astro-ph.CO↗