Constraints on primordial isocurvature perturbations and spatial curvature by Bayesian model selection

We present posterior likelihoods and Bayesian model selection analysis for generalized cosmological models where the primordial perturbations include correlated adiabatic and cold dark matter isocurvature components. We perform nested sampling with flat and, for the first time, curved spatial geometries of the Universe, using data from the cosmic microwave background (CMB) anisotropies, the Union supernovae (SN) sample and a combined measurement of the integrated Sachs-Wolfe (ISW) effect. The CMB alone favors a 3% (positively correlated) isocurvature contribution in both the flat and curved cases. The non-adiabatic contribution to the observed CMB temperature variance is 0 < alpha_T < 7% at 98% CL in the curved case. In the flat case, combining the CMB with SN data artificially biases the result towards the pure adiabatic LCDM concordance model, whereas in the curved case the favored level of non-adiabaticity stays at 3% level with all combinations of data. However, the ratio of Bayes factors, or Delta ln(evidence), is more than 5 points in favor of the flat adiabatic LCDM model, which suggests that the inclusion of the 5 extra parameters of the curved isocurvature model is not supported by the current data. The results are very sensitive to the second and third acoustic peak regions in the CMB temperature angular power: therefore a careful calibration of these data will be required before drawing decisive conclusions on the nature of primordial perturbations. Finally, we point out that the odds for the flat non-adiabatic model are 1:3 compared to the curved adiabatic model. This may suggest that it is not much less motivated to extend the concordance model with 4 isocurvature degrees of freedom than it is to study the spatially curved adiabatic model.Comment: 15 pages, 5 figures. V2: References and future predictions added; accepted by PR

Primordial non-Gaussianity from two curvaton decays

We study a model where two scalar fields, that are subdominant during inflation, decay into radiation some time after inflation has ended but before primordial nucleosynthesis. Perturbations of these two curvaton fields can be responsible for the primordial curvature perturbation. We write down the full non-linear equations that relate the primordial perturbation to the curvaton perturbations on large scales, calculate the power spectrum of the primordial perturbation, and finally go to second order to find the non-linearity parameter, fNL. We find large positive values of fNL if the energy densities of the curvatons are sub-dominant when they decay, as in the single curvaton case. But we also find a large fNL even if the curvatons dominate the total energy density in the case when the inhomogeneous radiation produced by the first curvaton decay is diluted by the decay of a second nearly homogeneous curvaton. The minimum value min(fNL)=-5/4 which we find is the same as in the single-curvaton case.Comment: 20 pages, 5 figure

Unmodified Gravity

By relaxing the conventional assumption of a purely gravitational interaction between dark energy and dark matter, substantial alterations to the growth of cosmological structure can occur. In this work we focus on the homogeneous transfer of energy from a decaying form of dark energy. We present simple analytic solutions to the modified growth rates of matter fluctuations in these models, and demonstrate that neglecting physics within the dark sector may induce a significant bias in the inferred growth rate, potentially offering a false signature of modified gravity.Comment: 7 pages, 5 figures, new eq (7), changes reflect published versio

Interacting Dark Energy -- constraints and degeneracies

In standard cosmologies, dark energy interacts only gravitationally with dark matter. There could be a non-gravitational interaction in the dark sector, leading to changes in the effective DE equation of state, in the redshift dependence of the DM density and in structure formation. We use CMB, BAO and SNIa data to constrain a model where the energy transfer in the dark sector is proportional to the DE density. There are two subclasses, defined by the vanishing of momentum transfer either in the DM or the DE frame. We conduct a Markov-Chain Monte-Carlo analysis to obtain best-fit parameters. The background evolution allows large interaction strengths, and the constraints from CMB anisotropies are weak. The growth of DM density perturbations is much more sensitive to the interaction, and can deviate strongly from the standard case. However, the deviations are degenerate with galaxy bias and thus more difficult to constrain. Interestingly, the ISW signature is suppressed since the non-standard background evolution can compensate for high growth rates. We also discuss the partial degeneracy between interacting DE and modified gravity, and how this can be broken.Comment: 12 pages, 18 figures. Clarification on instabilities. Accepted by PR

Correlated Primordial Perturbations in Light of CMB and LSS Data

We use cosmic microwave background (CMB) and large-scale structure data to constrain cosmological models where the primordial perturbations have both an adiabatic and a cold dark matter (CDM) isocurvature component. We allow for a possible correlation between the adiabatic and isocurvature modes, and for different spectral indices for the power in each mode and for their correlation. We do a likelihood analysis with 11 independent parameters. We discuss the effect of choosing the pivot scale for the definition of amplitude parameters. The upper limit for the isocurvature fraction is 18% around a pivot scale k = 0.01 Mpc^{-1}. For smaller pivot wavenumbers the limit stays about the same. For larger pivot wavenumbers, very large values of the isocurvature spectral index are favored, which makes the analysis problematic, but larger isocurvature fractions seem to be allowed. For large isocurvature spectral indices n_iso > 2 a positive correlation between the adiabatic and isocurvature mode is favored, and for n_iso < 2 a negative correlation is favored. The upper limit to the nonadiabatic contribution to the CMB temperature variance is 7.5%. Of the standard cosmological parameters, determination of the CDM density $\omega_c$ and the sound horizon angle $\theta$ (or the Hubble constant $H_0$) are affected most by a possible presence of a correlated isocurvature contribution. The baryon density $\omega_b$ nearly retains its ``adiabatic value''.Comment: 20 pages, 21 figures (many in color

Correlated isocurvature perturbations from mixed inflaton–curvaton decay

We study cosmological perturbations in the case in which present-day matter consists of a mixture of inflaton and curvaton decay products. We calculate how the curvaton perturbations are transferred to its decay products in the general case when it does not behave like dust. Taking into account that the decay products of the inflaton can also have perturbations results in an interesting mixture of correlated adiabatic and isocurvature perturbations. In particular, negative correlation can improve the fit to the CMB data by lowering the angular power in the Sachs–Wolfe plateau without changing the peak structure. We do an 11-parameter fit to the WMAP data. We find that the best fit is not the ‘concordance model’, and that well-fitting models do not cluster around the best fit, so cosmological parameters cannot be reliably estimated. We also find that in our model the mean quadrupole (l = 2) power is l(l+1)Cl/2π = 1081 μK2, much lower than in the pure adiabatic ΛCDM model, which gives 1262 μK2.Peer reviewe

Testing distance duality with CMB anisotropies

We constrain deviations of the form T proportional to (1 + z)(1+epsilon) from the standard redshift-temperature relation, corresponding to modifying distance duality as D-L = (1 + z)(2(1+epsilon)) D-A. We consider a consistent model, in which both the background and perturbation equations are changed. For this purpose, we introduce a species of dark radiation particles to which photon energy density is transferred, and assume epsilon >= 0. The Planck 2015 release high multipole temperature plus low multipole data give the limit epsilon <4.5 x 10(-3) at 95% C.L. The main obstacle to improving this CMB-only result is strong degeneracy between and the physical matter densities omega(b) and omega(c). A constraint on deuterium abundance improves the limit to epsilon <1.8 x 10(-3). Adding the Planck high-multipole CMB polarisation and BAO data leads to a small improvement; with this maximal dataset we obtain epsilon <1.3 x 10(-3). This dataset constrains the present dark radiation energy density to at most 12% of the total photon plus dark radiation density. Finally, we discuss the degeneracy between dark radiation and the effective number of relativistic species N-eff, and consider the impact of dark radiation perturbations and allowing epsilon <0 on the results.Peer reviewe

Constraints on Scalar and Tensor Perturbations in Phenomenological and Two-field Inflation Models : Bayesian Evidences for Primordial Isocurvature and Tensor Modes

Peer reviewe

Correlated adiabatic and isocurvature CMB fluctuations in the wake of the WMAP

In general correlated models, in addition to the usual adiabatic component with a spectral index n_ad1 there is another adiabatic component with a spectral index n_ad2 generated by entropy perturbation during inflation. We extend the analysis of a correlated mixture of adiabatic and isocurvature CMB fluctuations of the WMAP group, who set the two adiabatic spectral indices equal. Allowing n_ad1 and n_ad2 to vary independently we find that the WMAP data favor models where the two adiabatic components have opposite spectral tilts. Using the WMAP data only, the 2-sigma upper bound for the isocurvature fraction f_iso of the initial power spectrum at k_0=0.05 Mpc^{-1} increases somewhat, e.g., from 0.76 of n_ad2 = n_ad1 models to 0.84 with a prior n_iso < 1.84 for the isocurvature spectral index. We also comment on a possible degeneration between the correlation component and the optical depth tau. Moreover, the measured low quadrupole in the TT angular power could be achieved by a strong negative correlation, but then one needs a large tau to fit the TE spectrum.Comment: 5 pages, 7 figures. V2: Added 2 figures and revised a bit the results section. This is a slightly longer version than the published one in PR

Novel CMB constraints on the α\alpha parameter in alpha-attractor models

Cosmological $\alpha$-attractors are a compelling class of inflationary models. They lead to universal predictions for large-scale observables, broadly independent from the functional form of the inflaton potential. In this work we derive improved analytical predictions for the large-scale observables, whose dependence on the duration of reheating and the parameter $\alpha$ is made explicit. We compare these with Planck and BICEP/Keck 2018 data in the framework of a Bayesian study, employing uniform logarithmic and linear priors for $\alpha$. Our improved universal predictions allow direct constraints on the duration of reheating. Furthermore, while it is well-known that CMB constraints on the tensor-to-scalar ratio can be used to place an upper bound on the $\alpha$ parameter, we demonstrate that including the $\alpha$-dependence of the scalar spectral tilt yields novel constraints on $\alpha$. In particular, for small $\alpha$, the scalar spectral tilt scales with $\log_{10}\alpha$, regardless of the specific potential shape. For decreasing $\alpha$, this eventually puts the models in tension with CMB measurements, bounding the magnitude of $\alpha$ from below. Therefore, in addition to the upper bound from the tensor-to-scalar ratio, we derive the first lower bound on the magnitude of $\alpha$ for $\alpha$-attractor T-models, $\log_{10}{\alpha} = -4.2^{+5.4}_{-8.6}$ at $95\%$ C.L. .Comment: version accepted for publication in JCA