arXiv subjects

P. Daniel Meerburg

Publications and source records attributed to P. Daniel Meerburg.

69 records · Page 4Linked to original sources

arXiv2015

Joint resonant CMB power spectrum and bispectrum estimation

We develop the tools necessary to assess the statistical significance of resonant features in the CMB correlation functions, combining power spectrum and bispectrum measurements. This significance is typically addressed by running a large number of simulations to derive the probability density function (PDF) of the feature-amplitude in the Gaussian case. Although these simulations are tractable for the power spectrum, for the bispectrum they require significant computational resources. We show that, by assuming that the PDF is given by a multi-variate Gaussian where the covariance is determined by the Fisher matrix of the sine and cosine terms, we can efficiently produce spectra that are statistically close to those derived from full simulations. By drawing a large number of spectra from this PDF, both for the power spectrum and the bispectrum, we can quickly determine the statistical significance of candidate signatures in the CMB, considering both single frequency and multi-frequency estimators. We show that for resonance models, cosmology and foreground parameters have little influence on the estimated amplitude, which allows to simplify the analysis considerably. A more precise likelihood treatment can then be applied to candidate signatures only. We also discuss a modal expansion approach for the power spectrum, aimed at quickly scanning through large families of oscillating models.

astro-ph.CO↗

arXiv2015

Optimal CMB estimators for bispectra from excited states

We propose optimal estimators for bispectra from excited states. Two common properties of such bispectra are the enhancement in the collinear limit, and the prediction of oscillating features. We review the physics behind excited states and some of the choices made in the literature. We show that the enfolded template is a good template in the collinear limit, but does poorly elsewhere, establishing a strong case for an improved estimator. Although the detailed scale dependence of the bispectra differs depending on various assumptions, generally the predicted bispectra are either effectively 1 or 2-dimensional and a simple Fourier basis suffices for accurate reconstruction. For an optimal CMB data analysis, combining all n-point functions, the choice for the excited state needs to be the same when computing power spectrum, bispectrum and higher order correlation functions. This has not always been the case, which could lead to wrong conclusions. We calculate the bispectrum for different choices previously discussed for the power spectrum, setting up a consistent framework to search for evidence of excited states in the CMB data.

astro-ph.CO↗

arXiv2015

Multi-wavelength constraints on the inflationary consistency relation

We present the first attempt to use a combination of CMB, LIGO, and PPTA data to constrain both the tilt and the running of primordial tensor power spectrum through constraints on the gravitational wave energy density generated in the early universe. Combining measurements at different cosmological scales highlights how complementary data can be used to test the predictions of early universe models including the inflationary consistency relation. Current data prefers a slightly positive tilt ($n_t = 0.06^{+0.63}_{-0.89}$) and a negative running ($n_{t, {\rm run}} < -0.22$) for the tensor power spectrum spectrum. Interestingly, the addition of direct gravitational wave detector data alone puts strong bounds on the tensor-to-scalar ratio $r < 0.2$ since the large positive tensor tilt preferred by the \textit{Planck} temperature power spectrum is no longer allowed. Adding the recently released BICEP2/KECK and Planck 353 GHz Polarization cross correlation data puts an even stronger bound $r<0.1$ . We comment on possible effects of a large positive tilt on the background expansion and show that depending on the assumptions regarding the UV cutoff ($k_{\rm UV}/k_* = 10^{24}$) of the primordial spectrum of gravitational waves, the strongest bounds on $n_t = 0.07^{+0.52}_{-0.80}$ are derived from this effect.

astro-ph.CO↗

arXiv2014

Testing Inflation with Large Scale Structure: Connecting Hopes with Reality

The statistics of primordial curvature fluctuations are our window into the period of inflation, where these fluctuations were generated. To date, the cosmic microwave background has been the dominant source of information about these perturbations. Large scale structure is however from where drastic improvements should originate. In this paper, we explain the theoretical motivations for pursuing such measurements and the challenges that lie ahead. In particular, we discuss and identify theoretical targets regarding the measurement of primordial non-Gaussianity. We argue that when quantified in terms of the local (equilateral) template amplitude $f_{\rm NL}^{\rm loc}$ ($f_{\rm NL}^{\rm eq}$), natural target levels of sensitivity are $Δf_{\rm NL}^{\rm loc, eq.} \simeq 1$. We highlight that such levels are within reach of future surveys by measuring 2-, 3- and 4-point statistics of the galaxy spatial distribution. This paper summarizes a workshop held at CITA (University of Toronto) on October 23-24, 2014.

astro-ph.CO↗

arXiv2014

An optimal estimator for resonance bispectra in the CMB

We propose an (optimal) estimator for a CMB bispectrum containing logarithmically spaced oscillations. There is tremendous theoretical interest in such bispectra, and they are predicted by a plethora of models, including axion monodromy models of inflation and initial state modifications. The number of resolved logarithmical oscillations in the bispectrum is limited due to the discrete resolution of the multipole bispectrum. We derive a simple relation between the maximum number of resolved oscillations and the frequency. We investigate several ways to factorize the primordial bispectrum, and conclude that a one dimensional expansion in the sum of the momenta $\sum k_i = k_t$ is the most efficient and flexible approach. We compare the expansion to the exact result in multipole space and show for $ω_{\rm eff}=100$ that $\mathcal{O}(10^3)$ modes are sufficient for an accurate reconstruction. We compute the expected $σ_{f_{\rm NL}}$ and find that within an effective field theory (EFT) the overall signal to noise scales as $S/N\propto ω^{3/2}$. Using only the temperature data we find $S/N\sim\mathcal{O}(1-10^2)$ for the frequency domain set by the EFT.

astro-ph.CO↗

arXiv2014

Alleviating the tension at low multipole through Axion Monodromy

There exists some tension on large scales between the Planck data and the LCDM concordance model of the Universe, which has been amplified by the recently claimed discovery of non-zero tensor to scalar ratio $r$. At the same time, the current best-fit value of $r$ suggests large field inflation delta phi>M_p, which requires a UV complete description of inflation. A very promising working example that predicts large tensor modes and can be UV completed is axion monodromy inflation. This realization of inflation naturally produces oscillating features, as consequence of a broken shift symmetry. We analyse a combination of Planck, ACT, SPT, WMAP low l polarization and BICEP2 data, and show a long wavelength feature from a periodic potential can alleviate the tension at low multipoles with an improvement delta chi^2 ~2.5-4 per degree of freedom, depending on the level of foreground subtraction. As with an introduction of running, one expects that any scale dependence should lead to a worsened fit at high multipoles. We show that the logarithmic nature of the axion feature in combination with a tilt n_s~1 allows the fit to be identical to a no feature model at the 2 percent level on scales 100 =< l =<3500, and quite remarkable actually slightly improves the fit at scales l >2000. We also consider possible unremoved dust foregrounds and show that including these hardly changes the best-fit parameters. Our analysis suggests an axion decay constant of f/M_p ~O(.01). We discuss how Planck measurements of the TE and EE spectra can further constrain axion monodromy inflation with such a large feature. A measurement of the large scale structure power spectrum is even more promising, as the effect is much bigger since the tensor modes do not affect the large scales. At the same time, a feature could also lead to a lower sigma8, lifting the tension between CMB and SZ constraints on sigma8.

astro-ph.CO↗

arXiv2014

Searching for oscillations in the primordial power spectrum

A small deviation from scale invariance in the form of oscillations in the primordial correlation spectra has been predicted by various cosmological models. In this paper we review a recently developed method to search for these features in the data in a more effective way. By Taylor expanding the small features around the 'background' cosmology, we have shown we are able to improve the search for these features compared to previous analyses. In this short paper we will extend that work by combining this method with a multi nested sampler. We recover our previous findings and are able to do so in 192 CPU hours. We will also briefly discuss the possibility of a long wavelength feature in the data to alleviate some tension between CMB data and the LCDM+r concordance cosmology.

astro-ph.CO↗

arXiv2014

Searching for Oscillations in the Primordial Power Spectrum: Constraints from Planck (Paper II)

We apply our recently developed code to search for resonance features in the Planck CMB temperature data. We search both for log spaced oscillations or linear spaced oscillations and compare our findings with results of our WMAP9 analysis and the Planck team analysis. While there are hints of log spaced resonant features present in the WMAP9 data, the significance of these features weaken with more data. With more accurate small scale measurements, we also find that the best fit frequency has shifted and the amplitude has been reduced. We confirm the presence of a several low frequency peaks, earlier identified by the Planck team, but with a better improvement of fit (delta chi^2 ~ 12). We further investigate this improvement by allowing the lensing potential to vary as well, showing mild correlation between the amplitude of the oscillations and the lensing amplitude. We find that the improvement of the fit increases even more (delta chi^2 ~ 14) for the low frequencies that modify the spectrum in a way that mimics the lensing effect. Since these features were not present in the WMAP data, they are primarily due to better measurements of Planck at small angular scales. For linear spaced oscillations we find a maximum delta chi^2 ~ 13 scanning two orders of magnitude in frequency space, and the biggest improvements are at extremely high frequencies. We recover a best fit frequency very close to the one found in WMAP9, which confirms that the fit improvement is driven by low l. Further comparisons with WMAP9 show Planck contains many more features, both for linear and log space oscillations, but with a smaller improvement of fit. We discuss the improvement as a function of the number of modes and study the effect of the 217 GHz map, which appears to drive most of the improvement for log spaced oscillations. We conclude that none of the detected features are statistically significant.

astro-ph.CO↗

arXiv2013

A new light on 21 cm intensity fluctuations from the dark ages

Fluctuations of the 21 cm brightness temperature before the formation of the first stars hold the promise of becoming a high-precision cosmological probe in the future. The growth of over densities is very well described by perturbation theory at that epoch and the signal can in principle be predicted to arbitrary accuracy for given cosmological parameters. Recently, Tseliakhovich and Hirata pointed out a previously neglected and important physical effect, due to the fact that baryons and cold dark matter (CDM) have supersonic relative velocities after recombination. This relative velocity suppresses the growth of matter fluctuations on scales $k \sim 10-10^3$ Mpc$^{-1}$. In addition, the amplitude of the small-scale power spectrum is modulated on the large scales over which the relative velocity varies, corresponding to $k \sim 0.005-1$ Mpc$^{-1}$. In this paper, the effect of the relative velocity on 21 cm brightness temperature fluctuations from redshifts $z \geq 30$ is computed. We show that the 21 cm power spectrum is affected on ${\it most}$ scales. On small scales, the signal is typically suppressed several tens of percent, except for extremely small scales ($k \gtrsim 2000$ Mpc$^{-1}$) for which the fluctuations are boosted by resonant excitation of acoustic waves. On large scales, 21 cm fluctuations are enhanced due to the non-linear dependence of the brightness temperature on the underlying gas density and temperature. The enhancement of the 21 cm power spectrum is of a few percent at $k \sim 0.1$ Mpc$^{-1}$ and up to tens of percent at $k \lesssim 0.005$ Mpc$^{-1}$, for standard $Λ$CDM cosmology. In principle this effect allows to probe the small-scale matter power spectrum not only through a measurement of small angular scales but also through its effect on large angular scales.

astro-ph.CO↗

arXiv2013

Searching for Oscillations in the Primordial Power Spectrum: Perturbative Approach (Paper I)

In this first of two papers, we present a new method for searching for oscillatory features in the primordial power spectrum. A wide variety of models predict these features in one of two different flavors: logarithmically spaced oscillations and linearly spaced oscillations. The proposed method treats the oscillations as perturbations on top of the scale-invariant power spectrum, allowing us to vary all cosmological parameters. This perturbative approach reduces the computational requirements for the search as the transfer functions and their derivatives can be precomputed. We show that the most significant degeneracy in the analysis is between the distance to last scattering and the overall amplitude at low frequencies. For models with logarithmic oscillations, this degeneracy leads to an uncertainty in the phase. For linear spaced oscillations, it affects the frequency of the oscillations. In this first of two papers, we test our code on simulated Planck-like data, and show we are able to recover fiducial input oscillations with an amplitude of a few times order 10^{-2}. We apply the code to WMAP9-year data and confirm the existence of two intriguing resonant frequencies for log spaced oscillations. For linear spaced oscillations we find a single resonance peak. We use numerical simulations to assess the significance of these features and conclude that the data do not provide compelling evidence for the existence of oscillatory features in the primordial spectrum.

astro-ph.CO↗

arXiv2012

Observational Constraints on Gauge Field Production in Axion Inflation

Models of axion inflation are particularly interesting since they provide a natural justification for the flatness of the potential over a super-Planckian distance, namely the approximate shift-symmetry of the inflaton. In addition, most of the observational consequences are directly related to this symmetry and hence are correlated. Large tensor modes can be accompanied by the observable effects of a the shift-symmetric coupling $ϕF\tilde F$ to a gauge field. During inflation this coupling leads to a copious production of gauge quanta and consequently a very distinct modification of the primordial curvature perturbations. In this work we compare these predictions with observations. We find that the leading constraint on the model comes from the CMB power spectrum when considering both WMAP 7-year and ACT data. The bispectrum generated by the non-Gaussian inverse-decay of the gauge field leads to a comparable but slightly weaker constraint. There is also a constraint from mu-distortion using TRIS plus COBE/FIRAS data, but it is much weaker. Finally we comment on a generalization of the model to massive gauge fields. When the mass is generated by some light Higgs field, observably large local non-Gaussianity can be produced.

astro-ph.CO↗

arXiv2011

WMAP 7 Constraints on Oscillations in the Primordial Power Spectrum

We use the WMAP 7 data to place constraints on oscillations supplementing an almost scale-invariant primordial power spectrum. Such oscillations are predicted by a variety of models, some of which amount to assuming there is some non-trivial choice of the vacuum state at the onset of inflation. In this paper we will explore data-driven constraints on two distinct models of initial state modifications. In both models the frequency, phase and amplitude are degrees of freedom of the theory for which the theoretical bounds are rather weak: both the amplitude and frequency have allowed values ranging over several orders of magnitude. This requires many computationally expensive evaluations of the model CMB spectra and their goodness-of-fit, even in a Markov Chain Monte Carlo (MCMC), normally the most efficient fitting method for such a problem. To search more efficiently we first run a densely spaced grid, with only 3 varying parameters; the frequency, the amplitude and the baryon density. We obtain the optimal frequency and run an MCMC at the best fit frequency, randomly varying all other relevant parameters. To reduce the computational time of each power spectrum computation, we adjust both comoving momentum integration and spline interpolation (in l) as a function of frequency and amplitude of the primordial power spectrum. Applying this to the WMAP 7 data allows us to improve existing constraints on the presence of oscillations. We confirm earlier findings that certain frequencies can improve the fitting over a model without oscillations. For those frequencies we compute the posterior probability, allowing us to put some constraints on the primordial parameter space of both models.

astro-ph.CO↗

arXiv2010

Oscillations in the bispectrum

There exist several models of inflation that produce primordial bispectra that contain a large number of oscillations. In this paper we discuss these models, and aim at finding a method of detecting such bispectra in the data. We explain how the recently proposed method of mode expansion of bispectra might be able to reconstruct these spectra from separable basis functions. Extracting these basis functions from the data might then lead to observational constraints on these models.

astro-ph.CO↗

arXiv2010

Minimal cut-off vacuum state constraints from CMB bispectrum statistics

In this short note we translate the best available observational bounds on the CMB bispectrum amplitudes into constraints on a specific scale-invariant New Physics Hypersurface (NPH) model of vacuum state modifications, as first proposed by Danielsson, in general models of single-field inflation. As compared to the power spectrum the bispectrum constraints are less ambiguous and provide an interesting upper bound on the cut-off scale in general models of single-field inflation with a small speed of sound. This upper bound is incompatible with the power spectrum constraint for most of the parameter domain, leaving very little room for minimal cut-off vacuum state modifications in general single-field models with a small speed of sound.

hep-th↗

arXiv2009

Bispectrum signatures of a modified vacuum in single field inflation with a small speed of sound

Deviations from the Bunch-Davies vacuum during an inflationary period can leave a testable imprint on the higher-order correlations of the CMB and large scale structures in the Universe. The effect is particularly pronounced if the statistical non-Gaussianity is inherently large, such as in models of inflation with a small speed of sound, e.g. DBI. First reviewing the motivations for a modified vacuum, we calculate the non-Gaussianity for a general action with a small speed of sound. The shape of its bispectrum is found to most resemble the 'orthogonal' or 'local' templates depending on the phase of the Bogolyubov parameter. In particular, for DBI models of inflation the bispectrum can have a profound 'local' template feature, in contrast to previous results. Determining the projection into the observational templates allows us to derive constraints on the absolute value of the Bogolyubov parameter. In the small sound speed limit, the derived constraints are generally stronger than the existing constraint derived from the power spectrum. The bound on the absolute value of the Bogolyubov parameter ranges from the 10^-6 to the 10^-3 level for H/Λ_c = 10^-3, depending on the specific details of the model, the sound speed and the phase of the Bogolyubov parameter.

hep-th↗