Small Scale Cosmological Perturbations: An Analytic Approach

Abstract

Through analytic techniques verified by numerical calculations, we establish general relations between the matter and cosmic microwave background (CMB) power spectra and their dependence on cosmological parameters on small scales. Fluctuations in the CMB, baryons, cold dark matter (CDM), and neutrinos receive a boost at horizon crossing. Baryon drag on the photons causes alternating acoustic peak heights in the CMB and is uncovered in its bare form under the photon diffusion scale. Decoupling of the photons at last scattering and of the baryons at the end of the Compton drag epoch, freezes the diffusion-damped acoustic oscillations into the CMB and matter power spectra at different scales. We determine the dependence of the respective acoustic amplitudes and damping lengths on fundamental cosmological parameters. The baryonic oscillations, enhanced by the velocity overshoot effect, compete with CDM fluctuations in the present matter power spectrum. We present new exact analytic solutions for the cold dark matter fluctuations in the presence of a growth- inhibiting radiation {\it and} baryon background. Combined with the acoustic contributions and baryonic infall into CDM potential wells, this provides a highly accurate analytic form of the small-scale transfer function in the general case.

Revised accepted version; no changed results but several minor typos corrected; index & other roadmaps added. TeX + 20 Figs

References in corpus (1)

• Toward Understanding CMB Anisotropies and Their Implications

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• $f(R)$ gravity modifications: from the action to the data
• The signature of the scattering between dark sectors in large scale cosmic microwave background anisotropies
• Cosmological evolution of warm dark matter fluctuations I: Efficient computational framework with Volterra integral equations
• Inflessence: a phenomenological model for inflationary quintessence
• Searching for Signatures of Dark matter-Dark Radiation Interaction in Observations of Large-scale Structure
• The tight-coupling approximation for baryon acoustic oscillations
• Does accelerating universe indicates Brans-Dicke theory
• Ultra-compact structure in radio quasars as a cosmological probe: a revised study of the interaction between cosmic dark sectors
• Constraints on the exponential $f(R)$ model from latest Hubble parameter measurements
• Non-Nucleosynthetic Constraints on the Baryon Density and Other Cosmological Parameters
• Cosmology with decaying cosmological constant -- exact solutions and model testing
• Non-comoving Cosmology
• Energy Scale of Lorentz Violation in Rainbow Gravity
• Fluctuations in the Cosmic Microwave Background I: Form Factors and their Calculation in Synchronous Gauge
• Characterizing unknown systematics in large scale structure surveys
• Perturbed Recombination from Dark Matter Annihilation
• Extended $\Lambda$CDM model and viscous dark energy: A Bayesian analysis
• Spectral Distortion Anisotropy from Inflation for Primordial Black Holes
• Combining cosmological and local bounds on bimetric theory
• Robust constraints on dark energy and gravity from galaxy clustering data
• Confronting Tracker Field Quintessence with Data
• Can $f(R)$ gravity relieve $H_0$ and ${\sigma }_8$ tensions?
• Does jackknife scale really matter for accurate large-scale structure covariances?
• Constant surface gravity and density profile of dark matter
• Reconstructing the properties of dark energy from recent observations
• Dark Energy Survey Year 3 Results: Measurement of the Baryon Acoustic Oscillations with Three-dimensional Clustering
• The effect of different observational data on the constraints of cosmological parameters
• CMB in a box: causal structure and the Fourier-Bessel expansion
• Discrimination between Lambda-CDM, quintessence, and modified gravity models using wide area surveys
• Viscous universe with cosmological constant
• Constraining Thawing Quintessence
• Observational constraints on unified dark matter including Hubble parameter data
• Dark Matter Minihalos from Primordial Magnetic Fields
• Structure formation with primordial black holes: collisional dynamics, binaries, and gravitational waves
• The effective gravitational decoupling between dark matter and the CMB
• A semi-analytical approach to perturbations in mutated hilltop inflation
• Isocurvature Fluctuations in Tracker Quintessence Models
• Constraining dark energy via baryon acoustic oscillations in the (an)isotropic light-cone power spectrum
• Roles of Modified Chaplygin-Jacobi and Chaplygin-Abel Gases in FRW Universe
• Cosmological Constraints on Ghost Dark Energy in the Brans-Dicke Theory by Using MCMC Approach
• A Simple Analytic Treatment of Linear Growth of Structure with Baryon Acoustic Oscillations
• New cosmological constraints on the evolution of dark matter energy density
• Clustering with general photo-$z$ uncertainties: Application to Baryon Acoustic Oscillations
• Improved cosmological constraints on the curvature and equation of state of dark energy
• Testing Quintessence Axion Dark Energy with Recent Cosmological Results
• The miniJPAS survey: clusters and galaxy groups detection with AMICO
• Deconstructing the Planck TT Power Spectrum to Constrain Deviations from $\Lambda$CDM
• Impacts of different SNLS3 light-curve fitters on cosmological consequences of interacting dark energy models
• Comparing dark energy models with current observational data
• An updated analysis of two classes of f(R) theories of gravity
• New scenario of QCD axion clump formation I: Linear analysis
• Delayed Recombination and Standard Rulers
• Cosmological Constraints on the DGP braneworld model with Gamma-ray bursts
• Constraints from High-Precision Measurements of the Cosmic Microwave Background: The Case of Disintegrating Dark Matter with $\Lambda$ or Dynamical Dark Energy
• Distance Probes of Dark Energy
• Exploring the cosmological consequences of JLA supernova data with improved flux-averaging technique
• The effect of stellar encounters on the dark matter annihilation signal from prompt cusps
• Large Primordial Fluctuations in Gravitational Waves from Phase Transitions
• Towards realistic $f(T)$ models with nonminimal torsion-matter coupling extension
• Redshift Weights for Baryon Acoustic Oscillations : Application to Mock Galaxy Catalogs
• Thawing quintessence from the inflationary epoch to today
• CMB Spectral Distortion Constraints on Thermal Inflation
• An analytic approach to baryon acoustic oscillations
• A generalized mass-to-horizon relation: a new global approach to entropic cosmologies and its connection to $\Lambda$CDM
• UV Background-Induced Bifurcation of the Galactic Morphology
• Biases on cosmological parameter estimators from galaxy cluster number counts
• No evidence for the evolution of mass density power-law index $\gamma$ from strong gravitational lensing observation
• Is There a Detectable Vishniac Effect?
• Thin-shell wormholes constrained by cosmological observations
• Reconstructing a non-linear interaction in the dark sector with cosmological observations
• A unified TDiff invariant field theory for the dark sector
• Transient acceleration in $f(T)$ gravity
• $f(T)$ cosmology in the regime of quasar observations
• Forecast and analysis of the cosmological redshift drift
• Primordial magnetic fields generated by the non-adiabatic fluctuations at pre-recombination era
• Supernova, baryon acoustic oscillations, and CMB surface distance constraints on f(G) higher order gravity models
• Combined cosmological tests of a bivalent tachyonic dark energy scalar field model
• The Hubble constant and dark energy from cosmological distance measures
• The Phase of the BAO on Observable Scales
• Cosmological constraints on a unified dark matter-energy scalar field model with fast transition
• Analytic Spectra of CMB Anisotropies and Polarization Generated by Scalar Perturbations in Synchronous Gauge
• Varying constants entropic--$\Lambda$CDM cosmology
• Deviation From ΛCDM With Cosmic Strings Networks
• Consistency of nonlinear interacting ghost dark energy with recent observations
• Constraining the emergent dark energy models with observational data at intermediate redshift
• Kinetic theory of fermions in curved spacetime
• Observational tests of backreaction with recent data
• Constraints on $\Lambda (t)$-cosmology with power law interacting dark sectors
• Testing the nature of Dark Energy with Precision Cosmological constraints
• Calibrating the BAO scale using the CMB: Lifting the degeneracy between geometric and dynamic distortions using the sound horizon from the CMB
• Dark Energy Cosmology with the Alternative Cosmic Microwave Background Data
• Observational constraints on the braneworld model with brane-bulk energy exchange
• The Effects Of Relativistic Hidden Sector Particles on the Matter Power Spectrum
• Probing alternative cosmologies through the inverse distance ladder
• Figure of Merit and Different Combinations of Observational Data Sets
• Cosmological Constraints on Entropic Cosmology with Matter Creation
• Abundance and properties of dark radiation from the cosmic microwave background
• Constraints On Dark Energy Models From Galaxy Clusters and Gravitational Lensing Data
• DBI Galileon and Late time acceleration of the universe
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: constraints on the time variation of fundamental constants from the large-scale two-point correlation function
• SU(2)${}_{\mathrm{CMB}}$ and the cosmological model: angular power spectra
• Detecting baryon acoustic oscillations by 3d weak lensing
• Halting eternal acceleration with an effective negative cosmological constant
• Post-reionization HI 21-cm signal: A probe of negative cosmological constant
• Observational Constraints on Axions as Quintessence in String Theory
• Cosmological Constraint and Analysis on Holographic Dark Energy Model Characterized by the Conformal-age-like Length
• Cosmology with a Decaying Vacuum Energy Parametrization Derived from Quantum Mechanics
• Separation of instrumental and astrophysical foregrounds for mapping CMB anisotropies
• The role of $T_0$ in CMB anisotropy measurements
• Dark-energy dependent test of general relativity at cosmological scales
• Limits on dark matter annihilation in prompt cusps from the isotropic gamma-ray background
• Modelling spatial variations of the speed of light
• Current cosmological constraints on the curvature, dark energy and modified gravity
• Signature flips in time-varying $\Lambda (t)$ cosmological models with observational data
• On the concordance of cosmological data in the case of the generalized Chaplygin gas
• Constraining deviations from $\Lambda$CDM in the Hubble expansion rate
• Real-time cosmology with SKA
• The bispectrum of cosmic string temperature fluctuations including recombination effects
• Revisit of constraints on dark energy with Hubble parameter measurements including future redshift drift observations
• Suppression of Gravitational Structure Formation by Cosmological Accretion Heating
• Cosmological models with running cosmological term and decaying dark matter
• Why CMB physics?
• Unified dark matter and dark energy description in a chiral cosmological model
• Probing small-scale non-Gaussianity from anisotropies in acoustic reheating
• Tests of Standard Cosmology in Horava Gravity and Bayesian Evidence for a Closed Universe, and the Hubble Tension
• Signatures of the Baryon Acoustic Oscillations on the Convergence Power Spectrum of Weak lensing by Large Scale Structure
• Exploring evidence of interaction between dark energy and dark matter
• Gravitational particle production and the Hubble tension
• Bound Dark Energy: towards understanding the nature of the Dark Energy
• How an era of kination impacts substructure and the dark matter annihilation rate
• Modified Equations of State for Dark Energy and Observational Limitations
• New initial condition of the new agegraphic dark energy model
• Holographic field theory models of dark energy in interaction with dark matter
• Simulations of Gravitational Heating Due to Early Matter Domination
• Photo-z Quality Cuts and their Effect on the Measured Galaxy Clustering
• Calculation of Cosmic Background Radiation Anisotropies and Implications
• Cosmological implications of different baryon acoustic oscillation data
• Modelling Time-varying Dark Energy with Constraints from Latest Observations
• Plasma Perturbations and Cosmic Microwave Background Anisotropy in the Linearly Expanding Milne-like Universe
• The Alcock Paczynski test with 21cm intensity field
• SU(2)$_{\tiny\mbox{CMB}}$ at high redshifts and the value of $H_0$
• Impact of freeze-in on dark matter isocurvature
• Halos in Dark Ages: formation and chemistry
• Gamma-Ray Bursts and Dark Energy - Dark Matter interaction
• A circular polarimeter for the Cosmic Microwave Background
• Two-point statistics without bins: A continuous-function generalization of the correlation function estimator for large-scale structure
• Sub-horizon evolution of cold dark matter perturbations through dark matter-dark energy equivalence epoch
• A minimal set of invariants as a systematic approach to higher order gravity models: Physical and Cosmological Constraints
• Re-examining the role of curvature in the slowing down acceleration scenario
• The Einstein-Boltzmann equations revisited
• Cosmological constrains on fast transition Unified Dark Energy/Matter models
• Analysis cosmological tachyon and fermion model and observation data constraints
• Observational constraint on dynamical evolution of dark energy
• Effects of a Late Gravitational Transition on Gravitational Waves and Anticipated Constraints
• Interacting dark matter and cosmic acceleration
• Constraints on the $\Lambda$CDM model with redshift tomography
• Expansion and Growth of Structure Observables in a Macroscopic Gravity Averaged Universe
• Interacting dark energy collapse with matter components separation
• Probing Quintessence Potential with Future Cosmological Surveys
• Constraining dark energy using observational growth rate data
• Chi-square versus median statistics in SNIa data analysis
• Observational constraints to a unified cosmological model
• Multi-field TDiff theories for cosmology
• Investigating the Possibility of a Turning Point in the Dark Energy Equation of State
• Model-Independent Dark Energy Measurements from DESI DR2 and Planck 2015 Data
• Cosmological Model-independent Gamma-ray Bursts Calibration and its Cosmological Constraint to Dark Energy
• Time Variable Cosmological Constant from Renormalization Group Equations
• Fisher forecast for the BAO measurements from the CSST spectroscopic and photometric galaxy clustering
• The effect of curvature in thawing models
• Probing the cosmic acceleration from combinations of different data sets
• Observational constraints on G-corrected holographic dark energy using a Markov chain Monte Carlo method
• Toward More Realistic Mass Functions For Ultradense Dark Matter Halos
• Structure formation and CMBR anisotropy spectrum in the inflessence model
• Long-Wavelength Modes of Cosmological Scalar Fields
• Cosmological constraints for the Cosmic Defect theory
• Cosmological extrapolation of MOND
• Holographic Dark Energy with Curvature
• Smallest Halos in Thermal Wino Dark Matter
• Reconstruction of the interaction term between dark matter and dark energy using SNe Ia, BAO, CMB, H(z) and X-ray gas mass fraction
• Dark energy as an elastic strain fluid
• Can prompt cusps of WIMP dark matter be detected as individual gamma-ray sources?
• A Model for the Redshift-Space Galaxy 4-Point Correlation Function
• Signatures of Very Early Dark Energy in the Matter Power Spectrum
• Can the coincidence problem be solved by a cosmological model of coupled dark energy and dark matter?
• Refining the nonlinear modelling of primordial oscillatory features
• 21-cm Constraints on Dark Matter Annihilation after an Early Matter-Dominated Era
• Testing Dvali-Gabadadze-Porrati Gravity with Planck
• Distinguishing between inhomogeneous model and $\Lambda \text{CDM}$ model with the cosmic age method
• Comparing measures of the Hubble and BAO tensions in $\Lambda$CDM and possible solutions in $f(Q)$ gravity
• Redshift evolution of the Hubble constant: Constraints and new insights from an interacting dark energy model
• Parameters and pitfalls in dark energy models with time varying equation of state
• Effect of neutrino rest mass on ionization equilibrium freeze-out
• Probing Quintessence using BAO imprint on the cross-correlation of weak lensing and post-reionization HI 21 cm signal
• New parameterizations of generalized Chaplygin gas model constrained at background and perturbation levels
• A closer look at the cosmological implications of the $\Lambda$HDE model
• An analytical approach to the CMB anisotropies in a Spatially Closed background
• Local Limit of Nonlocal Gravity: A Teleparallel Extension of General Relativity
• Cosmological boost factor for dark matter annihilation at redshifts of $z=10$-$100$ using the power spectrum approach
• Impact of a primordial magnetic field on cosmic microwave background $B$ modes with weak lensing
• Accurate halo mass functions from the simplest excursion set theory
• Dark matter cooling during early matter-domination boosts sub-earth halos
• A Vishniac type contribution to the polarisation of the CMBR?
• Updated reduced CMB data and constraints on cosmological parameters
• Quintessence and tachyon dark energy in interaction with dark matter: Observational constraints and model selection
• Limits on Early Matter Domination from the Isotropic Gamma-Ray Background
• Baryon Acoustic Oscillations analyses with Density-Split Statistics
• Can MONDian vector theories explain the cosmic speed up ?
• Anisotropic cosmology using observational datasets: exploring via machine learning approaches
• Structure Formation with Warm White Noise: Effects of Finite Number Density and Velocity Dispersion in Particle and Wave Dark Matter
• Detecting Baryon Acoustic Oscillations in Dark Matter from Kinematic Weak Lensing Surveys
• A unification of RDE model and XCDM model
• Probing the independence within the dark sector in the fluid approximation
• Probing Cosmic Acceleration by Using Model-Independent Parametrizations and Three Kinds of Supernova Statistics Techniques
• Analytical warm dark matter power spectrum on small scales
• Enhanced Small-Scale Structure in the Cosmic Dark Ages
• Slow Diffusive Gravitational Instability Before Decoupling
• Cosmological Constraints on Neutrino Masses in a Second-Order CPL Dark Energy Model
• Ultradense Dark Matter Halos with Poisson Noise from Stellar-Mass Primordial Black Holes
• Dark aspects of massive spinor electrodynamics
• Bayesian analysis of the backreaction models
• Unimodular Theory of Gravity in Light of the Latest Cosmological Data
• Cosmological constraints from galaxy multi-tracers in the nearby Universe
• Linear and non-linear Modified Gravity forecasts with future surveys
• The Missing Mass Problem as a Manifestation of GR Contextuality
• Solving an Interacting Quintessence Model with a Sound Horizon Initial Condition and its Observational Constraints
• Artificial Neural Network Spectral Light Curve Template for Type Ia Supernovae and its Cosmological Constraints
• Fluids in cosmology
• Understanding CMB physics through the exploration of exotic cosmological models: a classroom study using CLASS
• Cosmology in warped massive gravity
• Gravity of Cosmological Perturbations in the CMB
• Solar System Tests of a New Class of $f(z)$ Theory
• Dissecting the $H_0$ and $S_8$ tensions with Planck + BAO + supernova type Ia in multi-parameter cosmologies
• Cosmic Microwave Background as a thermal gas of SU(2) photons: Implications for the high-z cosmological model and the value of $H_0$
• A semi-cosmographic approach to study cosmological evolution in phase space
• Ricci cosmology in light of astronomical data
• Cosmological constraints on the big bang quantum cosmology model
• On the baryon acoustic oscillation amplitude as a probe of radiation density
• Influence of Plasma Collective Effects on Cosmological Evolution
• Bayesian and Machine-Learning Analyses of Nonminimal $f(Q)$ Gravity and $H_0$ Tension
• The nonlinear equation of correlation function of galaxies in the expanding universe and the solution in linear approximation
• Cosmological Constraints on the DGP Model in light of DESI DR2 2025 Data
• From Geometry to Observation: Gravitational Waves and the Raychaudhuri Equation
• Issues and methods for CMB anisotropy data reduction
• On the energy flow of $\lambda$ in Hořava-Lifshitz cosmology
• A comparative study of emergent dark energy models
• Merging Galaxy Clusters and the Search for New Physics of Dark Matter: A Review
• Testing the effects from dark radiation
• Constraints on the gravitational potential from DESI DR2 BAO and its implications for the local void scenario
• The BAO scale -- how standard is the standard ruler?
• Observational and Thermodynamic aspects of one-dimensional Dark Energy EoS parametrization models
• Global Signals of the First Molecules from the Dark Ages in the Presence of Primordial Magnetic Fields
• Signatures of Primordial Gravitational Waves on the Large-Scale Structure of the Universe
• Probing dark energy with braneworld cosmology in the light of recent cosmological data
• Exploring the constraints on cosmological models with CosmoEJS