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Register a new userThe power spectrum on small scales: Robust constraints and comparing PBH methodologies
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We compare primordial black hole (PBH) constraints on the power spectrum and mass distributions using the traditional Press Schechter formalism, peaks theory, and a recently developed version of peaks theory relevant to PBHs. We show that, provided the PBH formation criteria and the power spectrum smoothing are treated consistently, the constraints only vary by $sim$10% between methods (a difference that will become increasingly important with better data). Our robust constraints from PBHs take into account the effects of critical collapse, the non-linear relation between $zeta$ and $delta$, and the shift from the PBH mass to the power spectrum peak scale. We show that these constraints are remarkably similar to the pulsar timing array (PTA) constraints impacting the black hole masses detected by the LIGO and Virgo, but that the $mu$-distortion constraints rule out supermassive black hole (SMBH) formation and potentially even the much lighter mass range of $sim$(1-100) $mathrm{M}_odot$ that LIGO/Virgo probes.
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Using the Reduced Relativistic Gas (RRG) model, we analytically determine the matter power spectrum for Warm Dark Matter (WDM) on small scales, $k>1 htext{/Mpc}$. The RRG is a simplified model for the ideal relativistic gas, but very accurate in the cosmological context. In another work, we have shown that, for typical allowed masses for dark matter particles, $m>5 text{keV}$, the higher order multipoles, $ell>2$, in the Einstein-Boltzmann system of equations are negligible on scales $k<10 htext{/Mpc}$. Hence, we can follow the perturbations of WDM using the ideal fluid framework, with equation of state and sound speed of perturbations given by the RRG model. We derive a Meszaros like equation for WDM and solve it analytically in radiation, matter and dark energy dominated eras. Joining these solutions, we get an expression that determines the value of WDM perturbations as a function of redshift and wavenumber. Then we construct the matter power spectrum and transfer function of WDM on small scales and compare it to some results coming from Lyman-$alpha$ forest observations. Besides being a clear and pedagogical analytical development to understand the evolution of WDM perturbations, our power spectrum results are consistent with the observations considered and the other determinations of the degree of warmness of dark matter particles.
We derive constraints on primordial power spectrum, for the first time, from galaxy UV luminosity functions (LFs) at high redshifts. Since the galaxy LFs reflect an underlying halo mass function which depends on primordial fluctuations, one can constrain primordial power spectrum, particularly on small scales. We perform a Markov Chain Monte Carlo analysis by varying parameters for primordial power spectrum as well as those describing astrophysics. We adopt the UV LFs derived from Hubble Frontier Fields data at $z = 6 -10$, which enable us to probe primordial fluctuations on the scales of $k sim 10 - 10^3~{rm Mpc}^{-1}$. Our analysis also clarifies how the assumption on cosmology such as primordial power spectrum affects the determination of astrophysical parameters.
We argue that the global signal of neutral hydrogen 21cm line can be a powerful probe of primordial power spectrum on small scales. Since the amplitude of small scale primordial fluctuations is important to determine the early structure formation and the timing when the sources of Lyman ${alpha}$ photons are produced, they in turn affect the neutral hydrogen 21cm line signal. We show that the information of the position of the absorption trough can severely constrain the small scale amplitude of primordial fluctuations once astrophysical parameters relevant to the 21cm line signal are fixed. We also discuss how the uncertainties of astrophysical parameters affect the constraints.
In this paper we show how effects from small scales enter the angular-redshift power spectrum $C_ell(z,z)$. In particular, we show that spectroscopic surveys with high redshift resolution are affected by small scales already on large angular scales, i.e. at low multipoles. Therefore, when considering the angular power spectrum with spectroscopic redshift resolution, it is important to account for non-linearities relevant on small scales even at low multipoles. This may also motivate the use of the correlation function instead of the angular power spectrum. These effects, which are very relevant for bin auto-correlations, but not so important for cross-correlations, are quantified in detail.
The concordance of the $Lambda$CDM cosmological model in light of current observations has been the subject of an intense debate in recent months. The 2018 Planck Cosmic Microwave Background (CMB) temperature anisotropy power spectrum measurements appear at face value to favour a spatially closed Universe with curvature parameter $Omega_K<0$. This preference disappears if Baryon Acoustic Oscillation (BAO) measurements are combined with Planck data to break the geometrical degeneracy, although the reliability of this combination has been questioned due to the strong tension present between the two datasets when assuming a curved Universe. Here, we approach this issue from yet another point of view, using measurements of the full-shape (FS) galaxy power spectrum, $P(k)$, from the Baryon Oscillation Spectroscopic Survey DR12 CMASS sample. By combining Planck data with FS measurements, we break the geometrical degeneracy and find $Omega_K=0.0023 pm 0.0028$. This constrains the Universe to be spatially flat to sub-percent precision, in excellent agreement with results obtained using BAO measurements. However, as with BAO, the overall increase in the best-fit $chi^2$ suggests a similar level of tension between Planck and $P(k)$ under the assumption of a curved Universe. While the debate on spatial curvature and the concordance between cosmological datasets remains open, our results provide new perspectives on the issue, highlighting the crucial role of FS measurements in the era of precision cosmology.
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