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In recent years, the formation of primordial black holes (PBH) in the early universe inflationary cosmology has garnered significant attention. One plausible scenario for primordial black hole (PBH) formation arises during the preheating stage following inflation. Notably, this scenario does not necessitate any ad-hoc fine-tuning of the scalar field potential. This paper focuses on the growth of primordial density perturbation and the consequent possibility of PBH formation in the preheating stage of the Starobinsky model for inflation. The typical mechanism for PBH formation during preheating is based on the collapse of primordial fluctuations that become super-horizon during inflation (type I) and re-enter the particle horizon in the different phases of cosmic expansion. In this work, we show that there exists a certain range of modes that remain in the sub-horizon (not exited) during inflation (type II modes) but evolve identically to type I modes if they fall into the instability band, leading to large density perturbation above the threshold and can potentially also contribute to the PBH formation. We detail the conditions determining the possible collapse of type I and/or type II modes whose wavelengths are larger than the Jeans length we derive from the effective sound speed of scalar field fluctuations. Since the preheating stage is an 'inflaton' (approximately) matter-dominated phase, we follow the framework of the critical collapse of fluctuations and compute the mass fraction using the well-known Press-Schechter and the Khlopov-Polnarev formalisms, and compare the two. Finally, we comment on the implications of our study for the investigations concerned with primordial accretion and consequent PBH contribution to the dark matter., Comment: 36 pages, 18 figures, version with extended results and discussion

We investigate the effect of Dark Stars (DSs) on the reionization history of the Universe, and the interplay between them and feedback due to Lyman-Werner (LW) radiation in reducing the Cosmic Microwave Background (CMB) optical depth to a value within the $\tau = 0.054 \pm 0.007$ range measured by Planck. We use a semi-analytic approach to evaluate reionization histories and CMB optical depths, which includes Population II (Pop II) stars in atomic cooling halos and Pop III stars in minihalos with LW feedback, preceded by a DS phase. We show that while LW feedback by itself can reduce the integrated optical depth to the last scattering surface to $\sim 0.05$ only if the Pop III star formation efficiency is less than $\sim 0.2\%$, the inclusion of a population of DSs can naturally lead to the measured CMB optical depth for much larger Pop III star formation efficiencies $\gtrsim 1\%$., Comment: 11 pages, 5 figures

Drake and Szekeres have extended the Newman-Janis algorithm to produce stationary axisymmetric spacetimes from general static spherically symmetric solutions of the Einstein equations. The algorithm mathematically generates an energy-momentum tensor for the rotating solution, but the rotating and nonrotating system may or may not represent the same physical system, in the sense of both being a perfect fluid, or an electromagnetic field, or a $\Lambda$-term, and so on. In Part I (arxiv:2104.02255), we compared the structure of the eigenvalues and eigenvectors of the rotating and nonrotating energy-momentum tensors (their Segre types) and looked for the existence of equations of state relating the rotating energy density and principal pressures for Kerr-Schild systems. Here we extend our analysis to general static spherically symmetric systems obtained according to the Drake-Szekeres generalization of the Newman-Janis algorithm. We find that these rotating systems can have almost all Segre types except [31] and [(31)]. Moreover, the Segre type of the spacetime can change severely in passing from the nonrotating to the rotating configurations, for example to $[11Z\bar{Z}]$ from seed systems which were initially [(111,1)]. We also find conditions dictating how many equations of state may exist in a Drake-Szekeres system., Comment: Replaced with updated version, published at Phys. Rev. D 104, 124067 (2021)

We solve Einstein's equations for slowly-rotating gravitational condensate stars (gravastars) up to second order in the rotation by expanding about the spherically symmetric gravastar with de Sitter interior and Schwarzschild exterior matched at their common horizon. Requiring that the perturbations are finite on the null surface reduces the exterior geometry to that of a Kerr black hole, implying that a slowly rotating gravastar cannot be distinguished from a Kerr black hole by any measurement or observation restricted to the macroscopic spacetime exterior to the horizon. We determine the interior solution, the surface stress tensor, and the Komar mass and angular momentum localized on the slowly rotating horizon surface. With the interior equation of state fixed at $p=-\rho$, finite junction conditions on the null horizon surface necessarily lead to an interior solution with a singular core, where the perturbative expansion breaks down. Comparison to other models and implications for more rapidly rotating gravastars are briefly discussed., Comment: Updated version, published as Phys. Rev. D 105, 024002

The Newman-Janis algorithm and its generalizations can be used mathematically to generate rotating solutions from nonrotating spherically-symmetric solutions within general relativity. The energy-momentum tensors of these solutions may or may not represent the same physical system, in the sense of both being a perfect fluid, or an electromagnetic field, or a $\Lambda$-term, and so on. In a series of two papers, we compare the structure of the eigenvalues and eigenvectors of the rotating and nonrotating energy-momentum tensors (their Segre types) and look for the existence of equations of state relating the energy density and the principal pressures. Part I covers Kerr-Schild systems, Part II more general systems. We find that there is a unique family of stationary axisymmetric Kerr-Schild systems that obey the same equation of state in both the rotating and nonrotating configurations. This family includes the Kerr and Kerr-Newman black holes, as well as rotating spacetimes whose mass function in the nonrotating limit contains a constrained superposition of a cloud of strings term, a Reissner-Nordstrom term, a cosmological constant term, and a Schwarzschild term. We describe the common equation of state relating energy density and pressure in this family of spacetimes and discuss some of its properties., Comment: Replaced with updated version, published at Phys. Rev. D 104, 124066 (2021)

The general form of the surface stress tensor of an infinitesimally thin shell located on a rotating null horizon is derived, when different interior and exterior geometries are joined there. Although the induced metric on the surface must be the same approached from either side, the first derivatives of the metric need not be. Such discontinuities lead to a Dirac $\delta$-distribution in the Einstein tensor localized on the horizon. For a general stationary axisymmetric geometry the surface stress tensor can be expressed in terms of two geometric invariants that characterize the surface, namely the discontinuities $[\kappa]$ and $[\cal J]$ of the surface gravity $\kappa$ and angular momentum density $\cal J$. The Komar energy and angular momentum are given in coordinates adapted to the Killing symmetries, and the surface contributions to each determined in terms of $[\kappa]$ and $[\cal J]$. Guided by these, a simple modification of the original Israel junction conditions is verified directly from the Einstein tensor density to give the correct finite result for the surface stress, when the normal $\boldsymbol n$ to the surface is allowed to tend continuously to a null vector. The relation to Israel's original junction conditions, which fail on null surfaces, is given. The modified junction conditions are suitable to the matching of a rotating `black hole' exterior to any interior geometry joined at the Kerr null horizon surface, even when the surface normal is itself discontinuous and the Barrab\`es-Israel formalism is also inapplicable. This joining on a rotating null horizon is purely of the matter shell type and does not contain a propagating gravitational shock wave., Comment: Replaced with updated version, published at Phys. Rev. D 105, 024001 (2022)

We provide a first systematic and quantitative discussion of the phenomenology of the non-relativistic effective Hamiltonian describing the nuclear scattering process for a Weakly Interacting Massive Particle (WIMP) of arbitrary spin $j_\chi$. To this aim we obtain constraints from a representative sample of present direct detection experiments assuming the WIMP-nucleus scattering process to be driven by each one of the 44 effective couplings that arise for $j_\chi\le$ 2. We find that a high value of the multipolarity $s\le 2 j_\chi$ of the coupling, related to the power of the momentum transfer $q$ appearing in the scattering amplitude, leads to a suppression of the expected rates and pushes the expected differential spectra to large recoil energies $E_R$. For $s\le$ 4 the effective scales probed by direct detection experiments can be suppressed by up to 5 orders of magnitude compared to the case of a standard spin-independent interaction. For operators with large $s$ the expected differential spectra can be pushed to recoil energies in the MeV range, with the largest part of the signal concentrated at $E_R\gtrsim$ 100 keV and a peculiar structure of peaks and minima arising when both the nuclear target and the WIMP are heavy. As a consequence the present bounds on the effective operators can be significantly improved by extending the recoil energy intervals to higher recoil energies. Our analysis assumes effective interaction operators that are irreducible under the rotation group. Such operators drive the interactions of high-multipole dark matter candidates, i.e. states that possess only the highest multipole allowed by their spin. As a consequence our analysis represents also the first phenomenological study of the direct detection of quadrupolar, octupolar, and hexadecapolar dark matter., Comment: 33 pages, 8 figures, 2 tables

We investigate the effects of producing dark matter by Hawking evaporation of primordial black holes (PBHs) in scenarios that may have a second well-motivated dark matter production mechanism, such as freeze-out, freeze-in, or gravitational production. We show that the interplay between PBHs and the alternative sources of dark matter can give rise to model-independent modifications to the required dark matter abundance from each production mechanism, which in turn affect the prospects for dark matter detection. In particular, we demonstrate that for the freeze-out mechanism, accounting for evaporation of PBHs after freeze-out demands a larger annihilation cross section of dark matter particles than its canonical value for a thermal dark matter. For mechanisms lacking thermalization due to a feeble coupling to the thermal bath, we show that the PBH contribution to the dark matter abundance leads to the requirement of an even feebler coupling. Moreover, we show that when a large initial abundance of PBHs causes an early matter-dominated epoch, PBH evaporation alone cannot explain the whole abundance of dark matter today. In this case, an additional production mechanism is required, in contrast to the case when PBHs are formed and evaporate during a radiation-dominated epoch., Comment: 16 pages, 2 figures

We introduce a systematic approach to characterize the most general non-relativistic WIMP-nucleus interaction allowed by Galilean invariance for a WIMP of arbitrary spin $j_\chi$ in the approximation of one-nucleon currents. Five nucleon currents arise from the nonrelativistic limit of the free nucleon Dirac bilinears. Our procedure consists in (1) organizing the WIMP currents according to the rank of the $2 j_\chi+1$ irreducible operator products of up to $2 j_\chi$ WIMP spin vectors, and (2) coupling each of the WIMP currents to each of the five nucleon currents. The transferred momentum $q$ appears to a power fixed by rotational invariance. For a WIMP of spin $j_\chi$ we find a basis of 4+20$j_\chi$ independent operators that exhaust all the possible operators that drive elastic WIMP-nucleus scattering in the approximation of one-nucleon currents. By comparing our operator basis, which is complete, to the operators already introduced in the literature we show that some of the latter for $j_\chi=1$ were not independent and some were missing. We provide explicit formulas for the squared scattering amplitudes in terms of the nuclear response functions, which are available in the literature for most of the targets used in WIMP direct detection experiments., Comment: 47 pages, 4 figures, 8 tables

We present a particular solution to the Einstein field equations that could arise as a magnetic monopole in the strong field limit of the Born-Infeld electrodynamics. We solve its geodesics exactly and show that they can mimic the gravitational lensing of a singular isothermal sphere, but with matter and radiation following the same trajectories. This solution has previously been called "cloud of strings" or "string hedgehog," and has appeared as the limit of a global O(3) monopole.

We present a time-dependent uniform-density interior Schwarzschild solution, an exact solution to the Einstein field equations. Our solution describes the collapse (or the time-reversed expansion) of an object from an infinite radius to an intermediate radius of 9/8 of the Schwarzschild radius, at which time a curvature singularity appears at the origin, and then continues beyond the singularity to a gravastar with radius equal to the Schwarzschild radius.

Dark energy stars are finite size astrophysical objects with an interior equation of state typical of dark energy. Examples are self-gravitating false vacuum bubbles, vacuum non-singular black holes, and gravastars. We present a time-dependent solution of Einstein's field equations that describes the collapse of a spherical system from an initial state of positive pressure to a final state with a dark energy core. Our solution has no singularities, no event horizons, and does not violate the weak or null energy conditions., Comment: Replaced with published version

We re-examine the case of anapole dark matter as an explanation for the DAMA annual modulation in light of the DAMA/LIBRA-phase2 results and improved upper limits from other DM searches. If the WIMP velocity distribution is assumed to be a Maxwellian, anapole dark matter is unable to provide an explanation of the DAMA modulation compatible with the other searches. Nevertheless, anapole dark matter provides a better fit to the DAMA-phase2 modulation data than an isoscalar spin-independent interaction, due to its magnetic coupling with sodium targets. A halo-independent analysis shows that explaining the DAMA modulation above 2 keVee in terms of anapole dark matter is basically impossible in face of the other null results, while the DAMA/LIBRA-phase2 modulation measurements below 2 keVee are marginally allowed. We conclude that in light of current measurements, anapole dark matter does not seem to be a viable explanation for the totality of the DAMA modulation., Comment: 16 pages, 6 figures. Updated to published version

The nature of dark matter remains one of the key science questions. Weakly Interacting Massive Particles (WIMPs) are among the best motivated particle physics candidates, allowing to explain the measured dark matter density by employing standard big-bang thermodynamics. We introduce here a radically new version of the widely used DarkSUSY package, which allows to compute the properties of such dark matter particles numerically. With DarkSUSY 6 one can accurately predict a large variety of astrophysical signals from dark matter, such as direct detection rates in low-background counting experiments and indirect detection signals through antiprotons, antideuterons, gamma rays and positrons from the Galactic halo, or high-energy neutrinos from the center of the Earth or of the Sun. For thermally produced dark matter like WIMPs, high-precision tools are provided for the computation of the relic density in the Universe today, as well as for the size of the smallest dark matter protohalos. Furthermore, the code allows to calculate dark matter self-interaction rates, which may affect the distribution of dark matter at small cosmological scales. Compared to earlier versions, DarkSUSY 6 introduces many significant physics improvements and extensions. The most fundamental new feature of this release, however, is that the code has been completely re-organized and brought into a highly modular and flexible shape. Switching between different pre-implemented dark matter candidates has thus become straight-forward, just as adding new - WIMP or non-WIMP - particle models or replacing any given functionality in a fully user-specified way. In this article, we describe the physics behind the computer package, along with the main structure and philosophy of this major revision of DarkSUSY. A detailed manual is provided together with the public release at www.darksusy.org., Comment: 58 pages with jcappub.sty, 6 figures. Main additions in version 6.1 are a new particle module for self-interacting dark matter, as well as the option to perform freeze-out calculations with arbitrary dark sector temperatures. Matches version published in JCAP

In the framework of a bimetric model, we discuss a relation between the (modified) Friedmann equations and a mechanical system similar to the quantum Hall effect problem. Firstly, we show how these modified Friedmann equations are mapped to an anisotropic two-dimensional charged harmonic oscillator in the presence of a constant magnetic field, with the frequencies of the oscillator playing the role of the cosmological constants. This problem has two energy scales leading to the identification of two different regimes, namely, one dominated by the cosmological constants, with exponential expansions for the scale factors, and the other dominated by a magnetic seed, which would be responsible for both a component of dark energy and a primordial magnetic field. The latter regime would be described by a (nonperturbative) mapping between the cosmological evolution and the quantum Hall effect., Comment: 4pp

If dark matter is composed of weakly interacting particles, Earth's orbital motion may induce a small annual variation in the rate at which these particles interact in a terrestrial detector. The DAMA collaboration has identified at a 9.3$\sigma$ confidence level such an annual modulation in their event rate over two detector iterations, DAMA/NaI and DAMA/LIBRA, each with $\sim7$ years of observations. We statistically examine the time dependence of the modulation amplitudes, which "by eye" appear to be decreasing with time in certain energy ranges. We perform a chi-squared goodness of fit test of the average modulation amplitudes measured\ by the two detector iterations which rejects the hypothesis of a consistent modulation amplitude at greater than 80\%, 96\%, and 99.6\% for the 2--4~keVee, 2--5~keVee and 2--6~keVee energy ranges, respectively. We also find that among the 14 annual cycles there are three $\gtrsim 3\sigma$ departures from the average in the 5-6~keVee energy range. In addition, we examined several phenomenological models for the time dependence of the modulation amplitude. Using a maximum likelihood test, we find that descriptions of the modulation amplitude as decreasing with time are preferred over a constant modulation amplitude at anywhere between 1$\sigma$ and 3$\sigma$, depending on the phenomenological model for the time dependence and the signal energy range considered. A time dependent modulation amplitude is not expected for a dark matter signal, at least for dark matter halo morphologies consistent with the DAMA signal. New data from DAMA/LIBRA--phase2 will certainly aid in determining whether any apparent time dependence is a real effect or a statistical fluctuation., Comment: 13 pages, 1 figure

The interaction between two initially causally disconnected regions of the universe is studied using analogies of non-commutative quantum mechanics and deformation of Poisson manifolds. These causally disconnect regions are governed by two independent Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) metrics with scale factors $a$ and $b$ and cosmological constants $\Lambda_a$ and $\Lambda_b$, respectively. The causality is turned on by positing a non-trivial Poisson bracket $[ {\cal P}_{\alpha}, {\cal P}_{\beta} ] =\epsilon_{\alpha \beta}\frac{\kappa}{G}$, where $G$ is Newton's gravitational constant and $\kappa $ is a dimensionless parameter. The posited deformed Poisson bracket has an interpretation in terms of 3-cocycles, anomalies and Poissonian manifolds. The modified FLRW equations acquire an energy-momentum tensor from which we explicitly obtain the equation of state parameter. The modified FLRW equations are solved numerically and the solutions are inflationary or oscillating depending on the values of $\kappa$. In this model the accelerating and decelerating regime may be periodic. The analysis of the equation of state clearly shows the presence of dark energy. By completeness, the perturbative solution for $\kappa \ll1 $ is also studied., Comment: New references added. To appear in Physical Review D

We present a halo-independent determination of the unmodulated signal corresponding to the DAMA modulation if interpreted as due to dark matter weakly interacting massive particles (WIMPs). First we show how a modulated signal gives information on the WIMP velocity distribution function in the Galactic rest frame, from which the unmodulated signal descends. Then we perform a mathematically-sound profile likelihood analysis in which we profile the likelihood over a continuum of nuisance parameters (namely, the WIMP velocity distribution). As a first application of the method, which is very general and valid for any class of velocity distributions, we restrict the analysis to velocity distributions that are isotropic in the Galactic frame. In this way we obtain halo-independent maximum-likelihood estimates and confidence intervals for the DAMA unmodulated signal. We find that the estimated unmodulated signal is in line with expectations for a WIMP-induced modulation and is compatible with the DAMA background+signal rate. Specifically, for the isotropic case we find that the modulated amplitude ranges between a few percent and about 25% of the unmodulated amplitude, depending on the WIMP mass., Comment: 34 pages, 11 figures. Discussion extended, one figure added. Factor of two corrected in all amplitudes. DAMA exposure changed from 13 to 14 cycles. Updated to published version

Directional dark matter detection attempts to measure the direction of motion of nuclei recoiling after having interacted with dark matter particles in the halo of our Galaxy. Due to Earth's motion with respect to the Galaxy, the dark matter flux is concentrated around a preferential direction. An anisotropy in the recoil direction rate is expected as an unmistakable signature of dark matter. The average nuclear recoil direction is expected to coincide with the average direction of dark matter particles arriving to Earth. Here we point out that for a particular type of dark matter, inelastic exothermic dark matter, the mean recoil direction as well as a secondary feature, a ring of maximum recoil rate around the mean recoil direction, could instead be opposite to the average dark matter arrival direction. Thus, the detection of an average nuclear recoil direction opposite to the usually expected direction would constitute a spectacular experimental confirmation of this type of dark matter., Comment: 8 pages, 3 figures

We show that any nonsingular (real or complex) square matrix can be factorized into a product of at most three normal matrices, one of which is unitary, another selfadjoint with eigenvalues in the open right half-plane, and the third one is normal involutory with a neutral negative eigenspace (we call the latter matrices normal neutral involutory). Here the words normal, unitary, selfadjoint and neutral are understood with respect to an indefinite inner product., Comment: 30 pages

There are various definitions of right and left polar decompositions of an $m\times n$ matrix $F \in \mathbb{K}^{m\times n}$ (where $\mathbb{K}=\mathbb{C}$ or $\mathbb{R}$) with respect to bilinear or sesquilinear products defined by nonsingular matrices $M\in \mathbb{K}^{m\times m}$ and $N\in \mathbb{K}^{n\times n}$. The existence and uniqueness of such decompositions under various assumptions on $F$, $M$, and $N$ have been studied. Here we introduce a new form of right and left polar decompositions, $F=WS$ and $F=S'W'$, respectively, where the matrix $W$ has orthonormal columns ($W'$ has orthonormal rows) with respect to suitably defined scalar products which are functions of $M$, $N$, and $F$, and the matrix $S$ is selfadjoint with respect to the same suitably defined scalar products and has eigenvalues only in the open right half-plane. We show that our right and left decompositions exist and are unique for any nonsingular matrices $M$ and $N$ when the matrix $F$ satisfies $(F^{[M,N]})^{[N,M]}=F$ and $F^{[M,N]}F$ ($FF^{[M,N]}$, respectively) is nonsingular, where $F^{[M,N]}=N^{-1} F^\# M$ with $F^\#=F^T$ for real or complex bilinear forms and $F^\#=\bar{F}^T$ for sesquilinear forms. When $M=N$, our results apply to nonsingular square matrices $F$. Our assumptions on $F$, $M$, and $N$ are in some respects weaker and in some respects stronger than those of previous work on polar decompositions., Comment: 22 pages

We study the kinetic decoupling of light (lesssim 10 GeV) magnetic dipole dark matter (DM). We find that present bounds from collider, direct DM searches, and structure formation allow magnetic dipole DM to remain in thermal equilibrium with the early universe plasma until as late as the electron-positron annihilation epoch. This late kinetic decoupling leads to a minimal mass for the earliest dark protohalos of thousands of solar masses, in contrast to the conventional weak scale DM scenario where they are of order 10^{-6} solar masses., Comment: 14 pages, 2 figures

Cosmological observations indicate that most of the matter in the Universe is Dark Matter. Dark Matter in the form of Weakly Interacting Massive Particles (WIMPs) can be detected directly, via its elastic scattering off target nuclei. Most current direct detection experiments only measure the energy of the recoiling nuclei. However, directional detection experiments are sensitive to the direction of the nuclear recoil as well. Due to the Sun's motion with respect to the Galactic rest frame, the directional recoil rate has a dipole feature, peaking around the direction of the Solar motion. This provides a powerful tool for demonstrating the Galactic origin of nuclear recoils and hence unambiguously detecting Dark Matter. Furthermore, the directional recoil distribution depends on the WIMP mass, scattering cross section and local velocity distribution. Therefore, with a large number of recoil events it will be possible to study the physics of Dark Matter in terms of particle and astrophysical properties. We review the potential of directional detectors for detecting and characterizing WIMPs., Comment: 57 pages, 23 figures, to appear in Physics Reports

We extend and correct a recently proposed maximum-likelihood halo-independent method to analyze unbinned direct dark matter detection data. Instead of the recoil energy as independent variable we use the minimum speed a dark matter particle must have to impart a given recoil energy to a nucleus. This has the advantage of allowing us to apply the method to any type of target composition and interaction, e.g. with general momentum and velocity dependence, and with elastic or inelastic scattering. We prove the method and provide a rigorous statistical interpretation of the results. As first applications, we find that for dark matter particles with elastic spin-independent interactions and neutron to proton coupling ratio $f_n/f_p=-0.7$, the WIMP interpretation of the signal observed by CDMS-II-Si is compatible with the constraints imposed by all other experiments with null results. We also find a similar compatibility for exothermic inelastic spin-independent interactions with $f_n/f_p=-0.8$., Comment: 26 pages and 15 figures. Some additional explanations added to the text in v3 with respect to v2

We compare the general effective theory of one-body dark matter nucleon interactions to current direct detection experiments in a global multidimensional statistical analysis. We derive exclusion limits on the 28 isoscalar and isovector coupling constants of the theory, and show that current data place interesting constraints on dark matter-nucleon interaction operators usually neglected in this context. We characterize the interference patterns that can arise in dark matter direct detection from pairs of dark matter-nucleon interaction operators, or from isoscalar and isovector components of the same operator. We find that commonly neglected destructive interference effects weaken standard direct detection exclusion limits by up to one order of magnitude in the coupling constants., Comment: 24 pages, 8 figures

We present a general expression for the values of the average kinetic energy and of the temperature of kinetic decoupling of a WIMP, valid for any cosmological model. We show an example of the usage of our solution when the Hubble rate has a power-law dependence on temperature, and we show results for the specific cases of kination cosmology and low- temperature reheating cosmology., Comment: 19 pages, 3 figures