arXiv subjects

Syksy Rasanen

Publications and source records attributed to Syksy Rasanen.

At least 19 recordsLinked to original sources

arXiv2026

Cosmic variance and ergodicity in finite systems with correlations

We consider the difference between ensemble and volume average in cosmology. It is known that for sufficiently weak long-range correlations the root mean square of the difference, which we call ergodicity bias, decays like $R^{-3/2}$ in the limit of large volume $R^3$. We calculate the condition this imposes on the power spectrum of a Gaussian random field. We quantify the bias for finite $R$, and show that the $R\to\infty$ limit is of little relevance for cosmological observations when the measured scales and correlations extend to the size of the observable universe. We consider curvature, density, and velocity perturbations. On large scales the bias is important in all three cases. For the density perturbations, which are observationally the most relevant, the relative bias first exceeds 100% at the separation $r=177$ Mpc, and is larger than 100% for all $r>560$ Mpc. It should be taken into account when comparing ensemble and volume averages for large-scale structure. The bias is also large for the cosmic microwave background temperature perturbations on large angular scales, but this is not relevant for observations, as their analysis does not involve volume averaging.

astro-ph.CO↗

arXiv2026

Inflation with the Gauss-Bonnet term in the Palatini formulation

We consider the Gauss-Bonnet term coupled to the inflaton in the Palatini formulation of gravity. Unlike in the metric formulation, the Gauss-Bonnet term is not always a total derivative. We solve for the connection and insert it into the action, exactly for the spatially flat FLRW spacetime, and using the gradient approximation and order reduction for a general spacetime. We consider three cases: when the connection is unconstrained, and when non-metricity or torsion is put to zero. In all cases, the leading order change to the inflaton kinetic has the same form as that generated by the Chern-Simons term, but a negative sign. The modification of the gravitational wave sector also has the same form as in the Chern-Simons case but with a negative sign, except possibly for zero torsion, depending on the coupling and the potential. Within the range of validity of our approximations, differences from the metric formulation are small unless the kinetic term flips sign or is close to doing so.

astro-ph.CO↗

arXiv2026

Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function

We study stochastic effects in viable ultra-slow-roll inflation models that produce primordial black holes. We consider asteroid, solar, and supermassive black hole seed masses. In each case, we simulate $10^8$ patches of the universe that may collapse into PBHs. In every patch, we follow $4\times10^4$ momentum shells to construct its spherically symmetric profile from first principles, without introducing a window function. We include the effects of critical collapse and the radiation era transfer function. The resulting compaction function profiles are very spiky due to stochastic kicks. This can enhance the PBH abundance by up to 36 orders of magnitude, depending on the mass range and collapse criterion. The PBH mass function shifts to higher masses and widens significantly. These changes may have a large effect on observational constraints of PBHs and make it possible to generate PBHs with a smaller amplitude of the power spectrum. However, convergence issues for the mass function remain. The results call for redoing collapse simulations to determine the collapse criterion for spiky profiles.

astro-ph.CO↗

arXiv2026

Inflation with the Chern-Simons term in the Palatini formulation

We consider the Chern--Simons term coupled to the inflaton in the Palatini formulation of general relativity. In contrast to the metric formulation, here the Chern--Simons term affects also the background evolution. We approximately solve for the connection, insert it back into the action, and reduce the order of the equations to obtain an effective theory in the gradient approximation. We consider three cases: when the connection is unconstrained, and when non-metricity or torsion is put to zero. In the first two cases, the inflaton kinetic term is modified with a term proportional to the square of the potential. For polynomial potentials dominated by the highest power of the field, the Chern--Simons term solves the problem that higher order corrections spoil the flatness of the potential. For Higgs inflation, the tensor-to-scalar ratio can be as large as the current observational bound, and the non-minimal coupling to the Ricci scalar can be as small as in the metric case. The Palatini contribution cures the known instability of the tensor modes due to the Chern--Simons term in the metric formulation.

astro-ph.CO↗

arXiv2026

The effect of matter discreteness on gravitational wave propagation in post-geometrical optics

The gravitational wave equation of motion includes direct coupling to the Riemann tensor. The curvature terms are usually neglected, but they can be large at the location of matter particles and impact the angular diameter distance. We apply the recently introduced post-geometrical optics approximation that includes curvature to gravitational wave propagation. Assuming that particles are localised within their Compton wavelength, the curvature due to electrons leads to a large effect on the angular diameter distance, but caustic formation invalidates the post-geometrical optics approximation. We conclude that the interesting regime of validity of the approximation is limited, as it ceases to apply when the curvature effects become large. Other methods are needed to evaluate the effect of curvature spikes, and the localisation of particles due to decoherence also needs further work.

astro-ph.CO↗

arXiv2025

Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation

We study the impact of stochastic noise on the generation of primordial black hole (PBH) seeds in ultra-slow-roll (USR) inflation with numerical simulations. We consider the non-linearity of the system by consistently taking into account the noise dependence on the inflaton perturbations, while evolving the perturbations on the coarse-grained background affected by the noise. We capture in this way the non-Markovian nature of the dynamics, and demonstrate that non-Markovian effects are subleading. Using the $ΔN$ formalism, we find the probability distribution $P(\mathcal{R})$ of the comoving curvature perturbation $\mathcal{R}$. We consider inflationary potentials that fit the CMB and lead to PBH dark matter with $i)$ asteroid, $ii)$ solar, or $iii)$ Planck mass, as well as $iv)$ PBHs that form the seeds of supermassive black holes. We find that stochastic effects enhance the PBH abundance by a factor of $\mathcal{O}(10)-\mathcal{O}(10^8)$, depending on the PBH mass. We also show that the usual approximation, where stochastic kicks depend only on the Hubble rate, either underestimates or overestimates the abundance by orders of magnitude, depending on the potential. We evaluate the gauge dependence of the results, discuss the quantum-to-classical transition, and highlight open issues of the application of the stochastic formalism to USR inflation.

astro-ph.CO↗

arXiv2025

Non-Gaussian tail of the curvature perturbation in stochastic ultra-slow-roll inflation: implications for primordial black hole production

We consider quantum diffusion in ultra-slow-roll (USR) inflation. Using the $ΔN$ formalism, we present the first stochastic calculation of the probability distribution $P(\mathcal{R})$ of the curvature perturbation during USR. We capture the non-linearity of the system, solving the coupled evolution of the coarse-grained background with random kicks from the short wavelength modes, simultaneously with the mode evolution around the stochastic background. This leads to a non-Markovian process from which we determine the highly non-Gaussian tail of $P(\mathcal{R})$. Studying the production of primordial black holes in a viable model, we find that stochastic effects during USR increase their abundance by a factor $\sim 10^5$ compared to the Gaussian approximation.

astro-ph.CO↗

arXiv2025

The effect of dark matter discreteness on light propagation

Light propagation in cosmology is usually studied in the geometrical optics approximation which requires the spacetime curvature to be much smaller than the light wavenumber. However, for non-fuzzy particle dark matter the curvature is concentrated in widely separated spikes at particle location. If the particle mass is localised within a Compton wavelength, then for masses $\gtrsim10^4$ GeV the curvature is larger than the energy of CMB photons. We consider a post-geometrical optics approximation that includes curvature. Photons gain a gravity-induced mass when travelling through dark matter, and light paths are not null nor geodesic. We find that the correction to the redshift is negligible. For the angular diameter distance, we show how the small average density emerges from the large local spikes when integrating along the light ray. We find that there can be a large correction to the angular diameter distance even for photon energies much larger than the curvature. This may allow to set a strong upper limit on the mass of dark matter particles. We discuss open issues related to the validity of our approximations.

astro-ph.CO↗

arXiv2025

Stability of non-degenerate Ricci-type Palatini theories

We study the stability of theories where the gravitational action has arbitrary algebraic dependence on the three first traces of the Riemann tensor: the Ricci tensor, the co-Ricci tensor, and the homothetic curvature tensor. We collectively call them Ricci-type tensors. We allow arbitrary coupling to matter. We consider the case when the connection is unconstrained, and the cases when either torsion or non-metricity is assumed to vanish. We find which combinations of Ricci-type tensors lead to new degrees of freedom around Minkowski and FLRW space, and when there are ghosts. None of the theories with new degrees of freedom are healthy, except for two previously known cases where there is a single new vector. We find that projective invariance is not a sufficient condition for a theory to be ghost-free.

gr-qc↗

arXiv2024

Primordial black hole compaction function from stochastic fluctuations in ultra-slow-roll inflation

We study the formation of primordial black holes (PBH) with ultra-slow-roll inflation when stochastic effects are important. We use the $ΔN$ formalism and simplify the stochastic equations with an analytical constant-roll approximation. Considering a viable inflation model, we find the spatial profile of the PBH compaction function numerically for each stochastic patch, without assumptions about Gaussianity or the radial profile. The stochastic effects that lead to an exponential tail for the density distribution also make the compaction function very spiky, unlike assumed in the literature. Naively using collapse thresholds found for smooth profiles, the PBH abundance is enhanced by up to a factor of $10^9$, and the PBH mass distribution is spread over three orders of magnitude in mass. The results point to a need to redo numerical simulations of PBH formation with spiky profiles.

astro-ph.CO↗

arXiv2024

Scalar fields with derivative coupling to curvature in the Palatini and the metric formulation

We study models where a scalar field has derivative and non-derivative couplings to the Ricci tensor and the co-Ricci tensor with a view to inflation. We consider both the metric formulation and the Palatini formulation. In the Palatini case, the couplings to the Ricci tensor and the Ricci scalar give the same result regardless of whether the connection is unconstrained or the non-metricity or the torsion is assumed to vanish. When the co-Ricci tensor is included, the unconstrained case and the zero torsion case are physically different. We reduce all the actions to the Einstein frame with minimally coupled matter, and find the leading order differences between the metric case and the Palatini cases.

gr-qc↗

arXiv2023

Palatini formulation for gauge theory: implications for slow-roll inflation

We consider a formulation of gauge field theory where the gauge field $A_α$ and the field strength $F_{αβ}$ are independent variables, as in the Palatini formulation of gravity. For the simplest gauge field action, this is known to be equivalent to the usual formulation. We add non-minimal couplings between $F_{αβ}$ and a scalar field, solve for $F_{αβ}$ and insert it back into the action. This leads to modified gauge field and scalar field terms. We consider slow-roll inflation and show that because of the modifications to the scalar sector, adding higher order terms to the inflaton potential does not spoil its flatness, unlike in the usual case. Instead they make the effective potential closer to quadratic. The modifications also solve the problem that Higgs inflation in the Palatini formulation is sensitive to higher order terms.

astro-ph.CO↗

arXiv2022

Tree-level unitarity in Higgs inflation in the metric and the Palatini formulation

We calculate the tree-level amplitudes for electrically neutral $2\to2$ scattering for the Standard Model Higgs doublet non-minimally coupled to the Ricci scalar. We consider both the metric and the Palatini formulation of gravity. We find the partial wave unitarity limit for a general background field value. Our results are in agreement with previous work. In the electroweak vacuum, tree-level unitarity is violated at $\sim M_\text{Planck}/ξ$ in the metric formulation, and at $\sim M_\text{Planck}/\sqrtξ$ in the Palatini formulation. In the inflationary large field background, the unitarity limit is at $\sim M_\text{Planck}/\sqrtξ$ in both formulations. We compare the unitarity violation energy to scales relevant during inflation. We also calculate a direct collider limit on $ξ$ in the Palatini formulation, $ξ<2.5\times10^{31}$.

astro-ph.CO↗

arXiv2022

Higgs inflation in the Palatini formulation with kinetic terms for the metric

We consider scalar field inflation in the Palatini formulation of general relativity. The covariant derivative of the metric is then non-zero. From the effective theory point of view it should couple to other fields. We write down the most general couplings between it and a scalar field that are quadratic in derivatives. We consider both the case when the torsion is determined by the field equations and the case when it is assumed to be zero a priori. We find the metric derivative terms can significantly modify inflationary predictions. We specialise to Higgs inflation and terms of only up to dimension 4. Transforming to the Einstein frame, we show that by tuning the coefficients of the new terms, we can generate various effective inflationary potentials, including quadratic, hilltop-type, $α$-attractor and inflection point. Some of these can give inflation in agreement with observations, including with a large tensor-to-scalar ratio, even if the non-minimal coupling is zero.

gr-qc↗

arXiv2021

Inflation with $R_{(αβ)}$ terms in the Palatini formulation

We study inflation with the most general non-degenerate gravitational action that depends on the symmetric part of the Ricci tensor coupled to a scalar field in the Palatini formulation of gravity. We use field redefinitions to shift the effect of the Ricci terms from gravity to the scalar field, and apply the result to slow-roll inflation. As examples, we consider actions quadratic and cubic in the Ricci tensor. In the quadratic case the results are similar to the case $R+αR^2$ that has been studied earlier: the tensor-to-scalar ratio $r$ can be suppressed by an arbitrary amount, while the scalar spectrum is unaffected. In the cubic case, $r$ can be suppressed by at most a factor of $2/9$, and the change in the scalar spectral index $n_s$ can be large.

astro-ph.CO↗

arXiv2021

Higgs inflation with the Holst and the Nieh-Yan term

The action of loop quantum gravity includes the Holst term and/or the Nieh-Yan term in addition to the Ricci scalar. These terms are expected to couple non-minimally to the Higgs. Thus the Holst and Nieh-Yan terms contribute to the classical equations of motion, and they can have a significant impact on inflation. We derive inflationary predictions in the parameter space of the non-minimal couplings, including non-minimally coupled terms up to dimension 4. Successful inflation is possible even with zero or negative coupling of the Ricci scalar. Notably, inflation supported by the non-minimally coupled Holst term alone gives almost the same observables as the original metric formulation plateau Higgs inflation. A non-minimally coupled Nieh-Yan term alone cannot give successful inflation. When all three terms are considered, the predictions for the spectral index and tensor-to-scalar ratio span almost the whole range probed by upcoming experiments. This is not true for the running of the spectral index, and many cases are highly tuned.

astro-ph.CO↗

arXiv2021

Critical point Higgs inflation in the Palatini formulation

We study Higgs inflation in the Palatini formulation with the renormalisation group improved potential in the case when loop corrections generate a feature similar to an inflection point. Assuming that there is a threshold correction for the Higgs quartic coupling $λ$ and the top Yukawa coupling $y_t$, we scan the three-dimensional parameter space formed by the two jumps and the non-minimal coupling $ξ$. The spectral index $n_s$ can take any value in the observationally allowed range. The lower limit for the running is $α_s>-3.5\times10^{-3}$, and $α_s$ can be as large as the observational upper limit. Running of the running is small. The tensor-to-scalar ratio is $2.2\times 10^{-17}<r<2\times10^{-5}$. We find that slow-roll can be violated near the feature, and a possible period of ultra-slow-roll contributes to the widening of the range of CMB predictions. Nevertheless, for the simplest tree-level action, the Palatini formulation remains distinguishable from the metric formulation even when quantum corrections are taken into account, because of the small tensor-to-scalar ratio.

astro-ph.CO↗

arXiv2020

Higgs-$R^2$ inflation -- full slow-roll study at tree-level

We consider Higgs inflation with an $αR^2$ term. It adds a new scalar degree of freedom, which leads to a two-field model of inflation. We do a complete slow-roll analysis of the three-dimensional parameter space of the $R^2$ coefficient $α$, the non-minimal coupling $ξ$ and the Higgs self-coupling $λ$. We find three classes of inflationary solutions, but only pure $R^2$ and attractor solutions fit observations. We find that pure Higgs inflation is impossible when the $R^2$ term is present regardless of how small $α$ is. However, we can have Higgs-like inflation, where the amplitude of the perturbations does not depend on $α$ and the predictions as a function of e-folds are the same as in Higgs inflation, although the inflationary trajectory is curved in field space. The spectral index is $0.939 < n_R < 0.967$, and constraining it to the observed range, the tensor-to-scalar ratio varies from $3.8\times10^{-3}$ to the maximum allowed by observations, $0.079$. Observational constraints on isocurvature perturbations contribute to these limits, whereas non-Gaussianity is automatically in the range allowed by observations.

astro-ph.CO↗