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Register a new userBlack Holes and WIMPs: All or Nothing or Something Else
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We consider constraints on primordial black holes (PBHs) in the mass range $( 10^{-18}text{-}10^{15} ),M_{odot}$ if the dark matter (DM) comprises weakly interacting massive particles (WIMPs) which form halos around them and generate $gamma$-rays by annihilations. We first study the formation of the halos and find that their density profile prior to WIMP annihilations evolves to a characteristic power-law form. Because of the wide range of PBH masses considered, our analysis forges an interesting link between previous approaches to this problem. We then consider the effect of the WIMP annihilations on the halo profile and the associated generation of $gamma$-rays. The observed extragalactic $gamma$-ray background implies that the PBH DM fraction is $f^{}_{rm PBH} lesssim 2 times 10^{-9},( m_{chi} / {rm TeV} )^{1.1}$ in the mass range $2 times 10^{-12},M_{odot},( m_{chi} / {rm TeV} )^{-3.2} lesssim M lesssim 5 times 10^{12},M_{odot},( m_{chi} / {rm TeV} )^{1.1}$, where $m_{chi}$ and $M$ are the WIMP and PBH masses, respectively. This limit is independent of $M$ and therefore applies for any PBH mass function. For $M lesssim 2times 10^{-12},M_{odot},( m_{chi}/ {rm TeV} )^{-3.2}$, the constraint on $f^{}_{rm PBH}$ is a decreasing function of $M$ and PBHs could still make a significant DM contribution at very low masses. We also consider constraints on WIMPs if the DM is mostly PBHs. If the merging black holes recently discovered by LIGO/Virgo are of primordial origin, this would rule out the standard WIMP DM scenario. More generally, the WIMP DM fraction cannot exceed $10^{-4}$ for $M > 10^{-9},M_{odot}$ and $m_{chi} > 10,$GeV. There is a region of parameter space, with $M lesssim 10^{-11},M_{odot}$ and $m_{chi} lesssim 100,$GeV, in which WIMPs and PBHs can both provide some but not all of the DM, so that one requires a third DM candidate.
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We briefly review main observational properties of fast radio bursts (FRBs) and discuss two most popular hypothesis for the explanation of these enigmatic intense millisecond radio flashes. FRBs most probably originate on extragalactic distances, and their rate on the sky is about a few thousand per day with fluences above $sim$~1~Jy~ms (or with fluxes larger than few tenths of Jy). Two leading scenarios describing these events include strong flares of magnetars and supergiant pulses of young radio pulsars with large rotational energy losses, correspondingly. At the moment, it is impossible to choose between these models. However, new telescopes can help to solve the puzzle of FRBs in near future.
It seems natural to ask why the universe exists at all. Modern physics suggests that the universe can exist all by itself as a self-contained system, without anything external to create or sustain it. But there might not be an absolute answer to why it exists. I argue that any attempt to account for the existence of something rather than nothing must ultimately bottom out in a set of brute facts; the universe simply is, without ultimate cause or explanation.
We study the statistical problem of estimating a rank-one sparse tensor corrupted by additive Gaussian noise, a model also known as sparse tensor PCA. We show that for Bernoulli and Bernoulli-Rademacher distributed signals and emph{for all} sparsity levels which are sublinear in the dimension of the signal, the sparse tensor PCA model exhibits a phase transition called the emph{all-or-nothing phenomenon}. This is the property that for some signal-to-noise ratio (SNR) $mathrm{SNR_c}$ and any fixed $epsilon>0$, if the SNR of the model is below $left(1-epsilonright)mathrm{SNR_c}$, then it is impossible to achieve any arbitrarily small constant correlation with the hidden signal, while if the SNR is above $left(1+epsilon right)mathrm{SNR_c}$, then it is possible to achieve almost perfect correlation with the hidden signal. The all-or-nothing phenomenon was initially established in the context of sparse linear regression, and over the last year also in the context of sparse 2-tensor (matrix) PCA, Bernoulli group testing, and generalized linear models. Our results follow from a more general result showing that for any Gaussian additive model with a discrete uniform prior, the all-or-nothing phenomenon follows as a direct outcome of an appropriately defined near-orthogonality property of the support of the prior distribution.
We consider the dark matter (DM) scenarios consisting of the mixture of WIMPs and PBHs and study how much fraction of the total DM can be PBHs. In such scenarios, PBHs can accrete the WIMPs and consequently enhance the heating and ionization in the intergalactic medium due to WIMP annihilations. We demonstrate that the CMB data can give the stringent bounds on the allowed PBH fraction which are comparable or even tighter than those from the gamma ray data depending on the DM masses. For instance, the MCMC likelihood analysis using the Planck CMB data leads to the bound on PBH DM fraction with respect to the total dark matter $f_{rm PBH} lesssim {cal O}( 10^{-10}sim 10^{-8})$ for the WIMP mass $m_{chi}sim {cal O}(10sim 10^3)$ GeV with the conventional DM annihilation cross section $langle sigma v rangle=3 times 10^{-26}~rm cm^3/s $. We also investigate the feasibility of the global 21-cm signal measurement to provide the stringent constraints on the PBH fraction.
We consider the linear regression problem of estimating a $p$-dimensional vector $beta$ from $n$ observations $Y = X beta + W$, where $beta_j stackrel{text{i.i.d.}}{sim} pi$ for a real-valued distribution $pi$ with zero mean and unit variance, $X_{ij} stackrel{text{i.i.d.}}{sim} mathcal{N}(0,1)$, and $W_istackrel{text{i.i.d.}}{sim} mathcal{N}(0, sigma^2)$. In the asymptotic regime where $n/p to delta$ and $ p/ sigma^2 to mathsf{snr}$ for two fixed constants $delta, mathsf{snr}in (0, infty)$ as $p to infty$, the limiting (normalized) minimum mean-squared error (MMSE) has been characterized by the MMSE of an associated single-letter (additive Gaussian scalar) channel. In this paper, we show that if the MMSE function of the single-letter channel converges to a step function, then the limiting MMSE of estimating $beta$ in the linear regression problem converges to a step function which jumps from $1$ to $0$ at a critical threshold. Moreover, we establish that the limiting mean-squared error of the (MSE-optimal) approximate message passing algorithm also converges to a step function with a larger threshold, providing evidence for the presence of a computational-statistical gap between the two thresholds.
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