We show that if a spectator linear isocurvature dark matter field degree of freedom has a constant mass through its entire evolution history, the maximum measurable isocurvature spectral index that is consistent with the current tensor-to-scalar ratio bound is about 2.4, even if experiments can be sensitive to a $10^{-6}$ contamination of the predominantly adiabatic power spectrum with an isocurvature power spectrum at the shortest observable length scales. Hence, any foreseeable future measurement of a blue isocurvature spectral index larger than about 2.4 may provide nontrivial evidence for dynamical degrees of freedom with time-dependent masses during inflation. The bound is not sensitive to the details of the reheating scenario and can be made mildly smaller if the tensor-to-scalar ratio is better constrained in the future.
We construct an axion model for generating isocurvature fluctuations with blue spectrum, n_{iso}=2-4, which is suggested by recent analyses of admixture of adiabatic and isocurvature perturbations with independent spectral indices, n_{ad} \ne n_{iso}. The distinctive feature of the model is that the spectrum is blue at large scales while scale invariant at small scales. This is naturally realized by the dynamics of the Peccei-Quinn scalar field.
Previous computations of strongly blue tilted axionic isocurvature spectra were computed in the parametric region in which the lightest time-dependent mass is smaller than the Hubble expansion rate during inflation, leading to an overdamped time evolution. Here we present the strongly blue tilted axionic isocurvature spectrum in an underdamped time evolution parametric regime. Somewhat surprisingly, there exist parametric regions with a strong resonant spectral behavior that leads to a rich isocurvature spectral shape. We focus on computing this resonant spectrum analytically in a large parame…
It is known that if the Peccei-Quinn symmetry breaking field is displaced from its minimum during inflation, the axion isocurvature spectrum is generically strongly blue tilted with a break transition to a flat spectrum. We fit this spectrum (incorporated into the "vanilla" $Λ$-CDM cosmological model) to the Planck and BOSS DR11 data and find a mild hint for the presence of axionic blue-tilted isocurvature perturbations. We find the best fit parameter region is consistent with all of the dark matter being composed of QCD axions in the context of inflationary cosmology with an expansion rate of…
Blue CDM-photon isocurvature perturbations are attractive in terms of observability and may be typical from the perspective of generic mass relations in supergravity. We present and apply three theorems useful for blue isocurvature perturbations arising from linear spectator scalar fields. In the process, we give a more precise formula for the blue spectrum associated with the axion model of 0904.3800, which can in a parametric corner give a factor of O(10) correction. We explain how a conserved current associated with Peccei-Quinn symmetry plays a crucial role and explicitly plot several exam…
Blue axion isocurvature perturbations are both theoretically well-motivated and interesting from a detectability perspective. These power spectra generically have a break from the blue region to a flat region. Previous investigations of the power spectra were analytic, which left a gap in the predicted spectrum in the break region due to the non-applicability of the used analytic techniques. We therefore compute the isocurvature spectrum numerically for an explicit supersymmetric axion model. We find a bump that enhances the isocurvature signal for this class of scenarios. A fitting function o…
We investigate cosmological signatures of uncorrelated isocurvature perturbations whose power spectrum is blue-tilted with spectral index 2<p<4. Such an isocurvature power spectrum can promote early formation of small-scale structure, notably dark matter halos and galaxies, and may thereby resolve the shortage of ionizing photons suggested by observations of galaxies at high redshifts (z~7-8) but that are required to reionize the universe at z~10. We mainly focus on how the formation of dark matter halos can be modified, and explore the connection between the spectral shape of CMB anisotropies…
We investigate the effects of isocurvature perturbations on the 21cm radiation from minihaloes (MHs) at high redshifts and examine constraints on the isocurvature amplitude and power spectrum using the next generation of radio telescopes such as the Square Kilometre Array. We find that there is a realistic prospect of observing the isocurvature imprints in the 21cm emission from MHs, but only if the isocurvature spectral index is close to $3$ (i.e., the spectrum is blue). When the isocurvature fraction increases beyond $\sim 10\%$ of the adiabatic component, we observe an unexpected decline in…
It is possible that the primordial non-Gaussianity is dominated by the higher order terms, such as that set by $g_{NL}$, not $f_{NL}$. In this paper we derive the spectral index and running of $g_{NL}$ from a single isocurvature scalar field. The scale dependences of non-Gaussianity parameters are detectable if the mass of isocurvature field is not too small compared to the Hubble parameter during inflation. In addition, we also apply our results to investigate the curvaton model with near quadratic potential in detail.
CMB Constraints on Pre-Inflationary Axion Dark Matter Isocurvature
Harvard-Smithsonian Center for Astrophysics（哈佛-史密森天体物理中心）；Brown University（布朗大学）；CERN（欧洲核子研究组织）；Nanjing Normal University（南京师范大学）；University of Chinese Academy of Sciences（中国科学院大学）
Bayesian model comparison penalizes models with more free parameters that are allowed to vary over a wide range, and thus offers the most robust method to decide whether some given data require new parameters. In this paper, we ask a simple question: do current cosmological data require extensions of the simplest single-field inflation models? Specifically, we calculate the Bayesian evidence of a totally anti-correlated isocurvature perturbation and a running spectral index of the scalar curvature perturbation. These parameters are motivated by recent claims that the observed temperature aniso…
We use CMB (WMAP and ACBAR), large scale structure (SDSS luminous red galaxies) and supernova (SNLS) data to constrain the possible contribution of CDM isocurvature modes to the primordial perturbation spectrum. We consider three different admixtures with adiabatic modes in a flat $Λ$CDM cosmology with no tensor modes: fixed correlations with a single spectral index; general correlations with a single spectral index; and general correlations with independent spectral indices for each mode. For fixed correlations, we verify the WMAP analysis for fully uncorrelated and anti-correlated modes, whi…
We argue that the 21-cm global signal can be a powerful probe of isocurvature perturbations, particularly for the ones with blue-tilted spectra. Although the 21-cm global signal is much affected by astrophysical processes, which give some uncertainties when cosmological models are investigated, recent results from HERA have constrained several astrophysical parameters, whose information can reduce the ambiguities originating from astrophysics. We show that the size and spectral tilt of isocurvature perturbations can be well inferred from the 21-cm global signal once the information on astrophy…
We examine bounds on adiabatic and isocurvature density fluctuations from $μ$-type spectral distortions of the cosmic microwave background (CMB). Studies of such distortion are complementary to CMB measurements of the spectral index and its running, and will help to constrain these parameters on significantly smaller scales. We show that a detection on the order of $μ\sim 10^{-7}$ would strongly be at odds with the standard cosmological model of a nearly scale-invariant spectrum of adiabatic perturbations. Further, we find that given the current CMB constraints on the isocurvature mode amplitu…
In this article we investigate the time evolution of the adiabatic(curvature) and isocurvature (entropy) spectral indices after end of inflation for all cosmological scales and two different initial conditions. For this purpose,we first extract an explicit equation for the time evolution of the comoving curvature perturbation (which may be known as the generalized Mukhanov-Sasaki equation). It shall be manifested that the evolution of adibatic spectral index severely depends on the intial conditions and just for the super-Hubble scales and adiabatic initial conditions is constat as be expected…
We discuss correlations among spectral observables as a new tool for differentiating between models for the primordial perturbation. We show that if generated in the isocurvature sector, a running of the scalar spectral index is correlated with the statistical properties of non-Gaussianities. In particular, we find a large running will inevitably be accompanied by a large running of $f_{\rm NL}$ and enhanced $g_{\rm NL}$, with $g_{\rm NL}\gg f_{\rm NL}^2$. If the tensor to scalar ratio is large, a large negative running must turn positive on smaller scales. Interestingly, the characteristic sc…
Recent analyses of cosmic microwave background surveys have revealed hints that there may be a non-trivial running of the running of the spectral index. If future experiments were to confirm these hints, it would prove a powerful discriminator of inflationary models, ruling out simple single field models. We discuss how isocurvature perturbations in multi-field models can be invoked to generate large runnings in a non-standard hierarchy, and find that a minimal model capable of practically realising this would be a two-field model with a non-canonical kinetic structure. We also consider altern…
Multifield models of inflation with nonminimal couplings are in excellent agreement with the recent results from {\it Planck}. Across a broad range of couplings and initial conditions, such models evolve along an effectively single-field attractor solution and predict values of the primordial spectral index and its running, the tensor-to-scalar ratio, and non-Gaussianities squarely in the observationally most-favored region. Such models also can amplify isocurvature perturbations, which could account for the low power recently observed in the CMB power spectrum at low multipoles. Future measur…
We show that the spectral energy distribution of relic gravitons mildly increases for frequencies smaller than the $μ$Hz and then flattens out whenever the refractive index of the tensor modes is dynamical during a quasi-de Sitter stage of expansion. For a conventional thermal history the high-frequency plateau ranges between the mHz and the audio band but it is supplemented by a spike in the GHz region if a stiff post-inflationary phase precedes the standard radiation-dominated epoch. Even though the slope is blue at intermediate frequencies, it may become violet in the MHz window. For a vari…
We present new constraints on the spectral index n_T of tensor fluctuations from the recent data obtained by the BICEP2 experiment. We found that the BICEP2 data alone slightly prefers a positive, "blue", spectral index with n_T=1.36\pm0.83 at 68 % c.l.. However, when a TT prior on the tensor amplitude coming from temperature anisotropy measurements is assumed we get n_T=1.67\pm0.53 at 68 % c.l., ruling out a scale invariant $n_T=0$ spectrum at more than three standard deviations. These results are at odds with current bounds on the tensor spectral index coming from pulsar timing, Big Bang Nuc…
We derive the spectral index of $f_{NL}$ and its running from isocurvature single field and investigate the curvaton models with a negative spectral index of $f_{NL}$ in detail. In particular, a numerical study of the axion-type curvaton model is illustrated, and we find that the spectral index of $f_{NL}$ is negative and its absolute value is maximized around $σ_*=πf/2$ for the potential $V(σ)=m^2f^2(1-\cos{σ\over f})$. The spectral index of $f_{NL}$ can be ${\cal O}(-0.1)$ for the axion-type curvaton model. A convincing detection of a positive $n_{f_{NL}}$ will rule out the axion-type curvat…
We examine the possibility of positive spectral index of the power spectrum of the primordial tensor perturbation produced during inflation in the light of the detection of the B-mode polarization by the BICEP2 collaboration. We find a blue tilt is in general possible when the slow-roll parameter decays rapidly. We present two known examples in which a positive spectral index for the tensor power spectrum can be obtained. We also briefly discuss other consistency tests for further studies on inflationary dynamics.
We investigate constraints on the spectral index of primordial gravitational waves (GWs), paying particular attention to a blue-tilted spectrum. Such constraints can be used to test a certain class of models of the early Universe. We investigate observational bounds from LIGO+Virgo, pulsar timing and big bang nucleosynthesis, taking into account the suppression of the amplitude at high frequencies due to reheating after inflation and also late-time entropy production. Constraints on the spectral index are presented by changing values of parameters such as reheating temperatures and the amount …
We explore whether multifield inflationary models make unambiguous predictions for fundamental cosmological observables. Focusing on $N$-quadratic inflation, we numerically evaluate the full perturbation equations for models with 2, 3, and $\mathcal{O}(100)$ fields, using several distinct methods for specifying the initial values of the background fields. All scenarios are highly predictive, with the probability distribution functions of the cosmological observables becoming more sharply peaked as $N$ increases. For $N=100$ fields, 95% of our Monte Carlo samples fall in the ranges $n_s \in (0.…
If the refractive index of the relic gravitons increases during a conventional stage of inflationary evolution the spectral energy density is blue at intermediate frequencies above the fHz and then flattens out after a knee that is typically smaller than the mHz. We investigate here the conditions leading to a sufficiently large spectral energy density in the nHz range where some peculiar signatures observed with the pulsar timing arrays have been recently attributed to cosmic gravitons. If these potential evidences are combined with the most recent bounds provided by wide-band interferometers…
We calculate the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ in a class of recently proposed two-field no-scale inflationary models in supergravity. We show that, in order to obtain correct predictions, it is crucial to take into account the coupling between the curvature and the isocurvature perturbations induced by the noncanonical form of the kinetic terms. This coupling enhances the curvature perturbation and suppresses the resulting tensor-to-scalar ratio to the per mille level even for values of the slow-roll parameter $ε\sim 0.01$. Beyond these particular models, we e…
We extend the method of Flow Equations to the Effective Field Theory framework of inflation, in order to investigate the observable predictions of a very broad class of inflationary models. Focusing our attention on the gravitational-wave sector, we derive a general expression for the consistency relation for effective models and provide a numerical implementation which allows to study how the generated models populate the $(r,nt)$ plane. We analyse $5 \times 10^{4}$ realizations of inflationary scenarios that respect the Null-Energy Condition ($ε> 0$) and $5 \times 10^{4}$ realizations that v…
The scale invariant scalar and tensor perturbations, which are predicted from inflation, are eigenmodes in the conformal coordinates. The 'out' observer in the de Sitter space observes a thermal spectrum with a Gibbons-Hawking temperature $H/2π$ of these 'Bunch-Davies' particles. The tensor power spectrum observed in experiments can have an imprint of the Gibbons-Hawking thermal distribution due to the mode mixing between 'in' state conformal coordinates and the coordinate frame of the observer. We find that the the Bunch-Davies modes appear as thermal modes to the asymptotic Minkowski observe…
In this paper, the optical spectra index - luminosity relationship is checked for the well-known 17 individual mapped QSOs, in order to give one more clearer conclusion on the so far conflicting dependence of the spectral index on the luminosity for AGN. Different from the global relationships based on the color difference (photometry parameters) for samples of AGN, the more reliable relationship is determined for the multi-epoch observed individual mapped QSOs with no contamination from the host galaxies, the line variabilities and the much different central properties. The final confirmed re…
The scalar-tensor Dirac-Born-Infeld (DBI) inflation scenario provides a simple mechanism to reduce the large values of the boost factor associated with single field models with DBI action, whilst still being able to drive 60 efolds of inflation. Using a slow-roll approach, we obtain an analytical expression for the spectral index of the perturbations and, moreover, determine numerically the regions of the parameter space of the model capable of giving rise to a power spectrum with amplitude and spectral index within the observed bounds. We find that regions that exhibit significant DBI effects…
