arXiv subjects

Mark P. Hertzberg

Publications and source records attributed to Mark P. Hertzberg.

At least 55 records · Page 3Linked to original sources

arXiv2020

Ultralight Scalar Decay and the Hubble Tension

We examine whether the Hubble tension, the mismatch between early and late measurements of $H_0$, can be alleviated by ultralight scalar fields in the early universe, and we assess its plausibility within UV physics. Since their energy density needs to rapidly redshift away, we explore decays to massless fields around the era of matter-radiation equality. We highlight a concrete implementation of ultralight pseudo-scalars, axions, that decay to an abelian dark sector. This scenario circumvents major problems of other popular realizations of early universe scalar models in that it uses a regular scalar potential that is quadratic around the minimum, instead of the extreme fine-tuning of many existing models. The idea is that the scalar is initially frozen in its potential until $H\sim m$, then efficient energy transfer from the scalar to the massless field can occur shortly after the beginning of oscillations due to resonance. We introduce an effective fluid model which captures the transition from the frozen scalar phase to the radiation dark sector phase. We perform a fit to a combined Planck 2018, BAO, SH$_0$ES and Pantheon supernovae dataset and find that the model gives $H_0=69.9_{-0.86}^{+0.84}$ km/s/Mpc with $Δχ^2 \approx -9$ compared to $Λ$CDM; while inclusions of other data sets may worsen the fit. Importantly, we find that large values of the coupling between fields is required for sufficiently rapid decay: For axion-gauge field models $ϕF\tilde{F}/Λ$ it requires $Λ\lesssim f/80$, where $2πf$ is the field range. We find related conclusions for scalar-scalar models $\simϕ\,χ^2$ and for models that utilize perturbative decays. We conclude that these sorts of ultralight scalar models that purport to alleviate the Hubble tension, while being reasonable effective field theories, require features that are difficult to embed within UV physics.

astro-ph.CO↗

arXiv2020

Symmetries from Locality. I. Electromagnetism and Charge Conservation

It is well known that a theory of the (i) Lorentz invariant and (ii) locally interacting (iii) two degrees of freedom of a massless spin 1 particle, the photon, leads uniquely to electromagnetism at large distances. In this work, we remove the assumption of (i) Lorentz boost invariance, but we still demand (ii) and (iii). We consider several broad classes of theories of spin 1, which in general explicitly violate Lorentz symmetry. We restrict to the familiar two degrees of freedom of the photon. We find that most theories lead to non-locality and instantaneous signaling at a distance. By demanding a mild form of locality (ii), namely that the tree-level exchange action is manifestly local, we find that the photon must still be sourced by a conserved charge with an associated internal symmetry. This recovers the central features of electromagnetism, although it does not by itself impose Lorentz boost symmetry. The case of gravitation dramatically improves the final conclusion and is reported in detail in our accompanying paper Part 2.

hep-th↗

arXiv2020

Symmetries from Locality. II. Gravitation and Lorentz Boosts

It is known that local, Lorentz invariant, unitary theories involving particles with spin 1 demand that the matter sector they couple to are organized by internal physical symmetries and the associated charge conservation, while spin 3/2 demands supersymmetry. However, the introduction of a spin 2 graviton does not obviously demand new symmetries of the matter sector (although it does demand a universal coupling). In this work we relax the assumption of Lorentz boost symmetry, while maintaining a basic notion of locality that there is no instantaneous signaling at a distance. This extends and complements our accompanying work in Part 1 on related issues for spin 1 particles in electromagnetism. In order to avoid potential problems with longitudinal modes of the graviton, we choose to project them out, leaving only two degrees of freedom. We study large classes of theories that a priori may violate Lorentz boost invariance. By requiring the tree-level exchange action be local, we find that consistency demands that the Lorentz boost symmetry must be satisfied by the graviton and the matter sector, and in turn we recover general relativity at this order of analysis.

hep-th↗

arXiv2020

Merger of Dark Matter Axion Clumps and Resonant Photon Emission

A portion of light scalar dark matter, especially axions, may organize into gravitationally bound clumps (stars) and be present in large number in the galaxy today. It is therefore of utmost interest to determine if there are novel observational signatures of this scenario. Work has shown that for moderately large axion-photon couplings, such clumps can undergo parametric resonance into photons, for clumps above a critical mass $M^{\star}_c$ determined precisely by some of us in Ref. [1]. In order to obtain a clump above the critical mass in the galaxy today would require mergers. In this work we perform full 3-dimensional simulations of pairs of axion clumps and determine the conditions under which mergers take place through the emission of scalar waves, including analyzing head-on and non-head-on collisions, phase dependence, and relative velocities. Consistent with other work in the literature, we find that the final mass from the merger $M^{\star}_{\text{final}}\approx 0.7(M^{\star}_1+M^{\star}_2)$ is larger than each of the original clump masses (for $M^{\star}_1\sim M^{\star}_2$). Hence, it is possible for sub-critical mass clumps to merge and become super-critical and therefore undergo parametric resonance into photons. We find that mergers are expected to be kinematically allowed in the galaxy today for high Peccei-Quinn scales, which is strongly suggested by unification ideas, although the collision rate is small. While mergers can happen for axions with lower Peccei-Quinn scales due to statistical fluctuations in relative velocities, as they have a high collision rate. We estimate the collision and merger rates within the Milky Way galaxy today. We find that a merger leads to a flux of energy on earth that can be appreciable and we mention observational search strategies.

hep-ph↗

arXiv2020

Gravitational Decoherence of Dark Matter

Decoherence describes the tendency of quantum sub-systems to dynamically lose their quantum character. This happens when the quantum sub-system of interest interacts and becomes entangled with an environment that is traced out. For ordinary macroscopic systems, electromagnetic and other interactions cause rapid decoherence. However, dark matter (DM) may have the unique possibility of exhibiting naturally prolonged macroscopic quantum properties due to its weak coupling to its environment, particularly if it only interacts gravitationally. In this work, we compute the rate of decoherence for light DM in the galaxy, where a local density has its mass, size, and location in a quantum superposition. The decoherence is via the gravitational interaction of the DM overdensity with its environment, provided by ordinary matter. We focus on relatively robust configurations: DM perturbations that involve an overdensity followed by an underdensity, with no monopole, such that it is only observable at relatively close distances. We use non-relativistic scattering theory with a Newtonian potential generated by the overdensity to determine how a probe particle scatters off of it and thereby becomes entangled. As an application, we consider light scalar DM, including axions. In the galactic halo, we use diffuse hydrogen as the environment, while near the earth, we use air as the environment. For an overdensity whose size is the typical DM de Broglie wavelength, we find that the decoherence rate in the halo is higher than the present Hubble rate for DM masses $m_a \lesssim 5 \times 10^{-7}$eV and in earth based experiments it is higher than the classical field coherence rate for $m_a \lesssim 10^{-6}$eV. When spreading of the states occurs, the rates can become much faster, as we quantify. Also, we establish that DM BECs decohere very rapidly and so are very well described by classical field theory.

gr-qc↗

arXiv2020

Implications for Dark Matter Direct Detection in the Presence of LIGO-Motivated Primordial Black Holes

We discuss formation of dark matter (DM) mini-halos around primordial black holes (PBHs) and its implication on DM direct detection experiments, including axion searches. Motivated by LIGO observations, we consider $f_{\textrm{DM}} \simeq 0.01$ as the fraction of DM in PBHs with masses $10 M_{\odot} - 70 M_{\odot}$. In this case, we expect the presence of dressed PBHs after Milky Way halo formation with mini-halo masses peaked around $M_{\textrm{halo}} \sim (50-55) M_{\textrm{PBH}}$. We analyze the effect of tidal forces acting on dressed PBHs within the Milky Way galaxy. In the solar neighborhood, the mini-halos are resistant against tidal disruption from the mean-field potential of the galaxy and encounters with stars, but they undergo a small level of disruption caused by disk shocking. The presence of mini-halos around LIGO-motivated PBHs today could reduce by half the local dark matter background. High-resolution simulations are encouraged. If the proposed scenario is realized, chances of direct detection of DM would decrease.

astro-ph.CO↗

arXiv2020

Eternal Inflation and Reheating in the Presence of the Standard Model Higgs Field

We study the details of eternal inflation in the presence of a spectator Higgs field within the framework of the minimal Standard Model. We have recently shown that in the presence of scalar field(s) which allow inflation only within a finite domain of field values, the universe reaches a steady state where the normalized distribution for the field(s) converges to a steady state distribution [1]. In this paper, we analyze this eternal inflation scenario with the renormalized Standard Model Higgs potential, since it also allows inflation in a finite domain, but turns over at high scales due to the running of the self-coupling, marking an exit from inflation. We compute the full steady state distribution for the Higgs using an integral evolution technique that we formulated in [1] and the fractal dimension of the universe. We then obtain a bound on the inflationary Hubble scale in order to have a large observable universe contained within the instability scale of $H\lesssim\mathcal{O}(10^9)$GeV depending on the top mass. Upon reheating of the universe, thermal fluctuations in the Higgs field could potentially pose another problem; however, we compute the rate of thermal bubble production and find that the probability of tunneling in the post-inflationary era is negligibly small even for very high reheat temperatures.

hep-ph↗

arXiv2020

Dark Matter and Naturalness

The Standard Model of particle physics is governed by Poincaré symmetry, while all other symmetries, exact or approximate, are essentially dictated by theoretical consistency with the particle spectrum. On the other hand, many models of dark matter exist that rely upon the addition of new added global symmetries in order to stabilize the dark matter particle and/or achieve the correct abundance. In this work we begin a systematic exploration into truly natural models of dark matter, organized by only relativity and quantum mechanics, without the appeal to any additional global symmetries, no fine-tuning, and no small parameters. We begin by reviewing how singlet dark sectors based on spin 0 or spin ${1\over2}$ should readily decay, while pure strongly coupled spin 1 models have an overabundance problem. This inevitably leads us to construct chiral models with spin ${1\over2}$ particles charged under confining spin 1 particles. This leads to stable dark matter candidates that are analogs of baryons, with a confinement scale that can be naturally $\mathcal{O}(100)$TeV. This leads to the right freeze-out abundance by annihilating into massless unconfined dark fermions. The minimal model involves a dark copy of $SU(3)\times SU(2)$ with 1 generation of chiral dark quarks and leptons. The presence of massless dark leptons can potentially give rise to a somewhat large value of $ΔN_{\text{eff}}$ during BBN. In order to not upset BBN one may either appeal to a large number of heavy degrees of freedom beyond the Standard Model, or to assume the dark sector has a lower reheat temperature than the visible sector, which is also natural in this framework. This reasoning provides a robust set of dark matter models that are entirely natural. Some are concrete realizations of the nightmare scenario in which dark matter may be very difficult to detect, which may impact future search techniques.

hep-ph↗

arXiv2019

Exploring the CMB Power Suppression in Canonical Inflation Models

There exists some evidence of a suppression in power in the CMB multipoles around $l \sim 20-30$. If taken seriously, this is in tension with the simplest inflationary models driven by a single scalar field with a standard type of slowly varying potential function $V(ϕ)$. Such potential functions generate a nearly scale invariant spectrum and so they do not possess the requisite suppression in power. In this paper we explore if canonical two-derivative inflation models, with a step-like feature in the potential, can improve agreement with data. We find that improvement can be made when one utilizes the standard slow-roll approximation formula for the power spectrum. However, we find that in order to have a feature in the power spectrum that is sufficiently localized so as to not significantly disrupt higher $l$ or lower $l$, the potential's step-like feature must be so sharp that the standard slow-roll approximations break down. This leads us to perform an exact computation of the power spectrum by solving for the Bunch-Davies mode functions numerically. We find that the corresponding CMB multipoles do not provide a good agreement with the data. We conclude that, unless there is fine-tuning, canonical inflation models do not fit this suppression in the data.

astro-ph.CO↗

arXiv2019

Quantum Fine-Tuning in Stringy Quintessence Models

We investigate the extent to which quintessence models for dark energy are fine-tuned in the context of recent swampland conjectures. In particular, the issue is whether there is a double fine-tuning in which both $V$ and $|\nabla V|$ are fine-tuned, or whether there is only a single fine-tuning due to the relation $|\nabla V|\sim V/M_{pl}$ arising naturally. We find that indeed this relation arises naturally in simple string compactifications for some scalars, such as the dilaton and volume modulus, when treated classically. However, we find that quantum effects can spoil this natural relation, unless the scalar is conformally coupled to the matter sector. Furthermore, it is well known that such conformal couplings are generically ruled out by fifth force tests. To avoid these fifth forces, an interesting proposal is to assume the scalar (quintessence) only couples to the hidden sector. However, we then find quantum corrections to $V$ from visible sector Standard Model particles generically spoil the relation. A possible way out of all these problems is to have the scalar conformally coupled to a dark sector that is an exact copy of the Standard Model. This ensures the relation $|\nabla V|\sim V/M_{pl}$ is maintained naturally even when matter particles run in the loop. However, we find that quantum corrections from quintessons or gravitons in the loop spoil the relation if the effective theory has a cutoff greater than $\sim 0.1$ GeV.

hep-th↗

arXiv2019

Vacuum Decay in Real Time and Imaginary Time Formalisms

We analyze vacuum tunneling in quantum field theory in a general formalism by using the Wigner representation. In the standard instanton formalism, one usually approximates the initial false vacuum state by an eigenstate of the field operator, imposes Dirichlet boundary conditions on the initial field value, and evolves in imaginary time. This approach does not have an obvious physical interpretation. However, an alternative approach does have a physical interpretation: in quantum field theory, tunneling can happen via classical dynamics, seeded by initial quantum fluctuations in both the field and its momentum conjugate, which was recently implemented in Ref. [1]. We show that the Wigner representation is a useful framework to calculate and understand the relationship between these two approaches. We find there are two, related, saddle point approximations for the path integral of the tunneling process: one corresponds to the instanton solution in imaginary time and the other one corresponds to classical dynamics from initial quantum fluctuations in real time. The classical approximation for the dynamics of the latter process is justified only in a system with many degrees of freedom, as can appear in field theory due to high occupancy of nucleated bubbles, while it is not justified in single particle quantum mechanics, as we explain. We mention possible applications of the real time formalism, including tunneling when the instanton vanishes, or when the imaginary time contour deformation is not possible, which may occur in cosmological settings.

hep-th↗

arXiv2019

Statistics of Inflating Regions in Eternal Inflation

We compute the distribution of sizes of inflating and non-inflating regions in an eternally inflating Universe. As a first illustrative problem, we study a simple scenario of an eternally inflating Universe in the presence of a massless scalar field $φ$ whose field values lie within some finite domain $φ\in(-φ_{cr},φ_{cr})$, with $\pmφ_{cr}$ marking the onset of thermalization/crunching. We compute many important quantities, including the fractal dimension, distribution of field values among inflating regions, and the number of inflating and non-inflating Hubble regions. With the aid of simulations in 1 spatial dimension, we show this eternally inflating Universe reaches a steady state in which average sizes of inflating regions grow only as a power law in the field's crunch value $\sim φ_{cr}^2$ (extension to higher dimensions is $\simφ^{2/D}$), contrary to a naive expectation of an exponential dependence. Furthermore, the distribution in sizes exhibits an exponential fall off for large distances (with an initial power law for inflating regions). We leave other interesting cases of more realistic potentials and time varying Hubble parameter for future work, with a possible application to the SM Higgs in the early Universe.

astro-ph.CO↗

arXiv2019

Counting of States in Higgs Theories

We enumerate the micro-states in Higgs theories, addressing (i) the number of vacuum states and (ii) the appropriate measure in the quantum path integral. To address (i) we explicitly construct the set of ground state wave-functionals in the field basis focussing on scalar modes $θ(x)$. Firstly, we show that in the limit in which the gauge coupling is zero, we obtain an infinite set of degenerate ground states at large volume distinguished by $θ(x)\toθ(x)+θ_0$, spontaneously breaking the global symmetry, as is well known. We then show that at finite gauge coupling there is a unique ground state at large volume since the wave-functional only depends on $\nablaθ$ in the IR, and we explain this at the level of the Lagrangian. Since gauge fields fall off exponentially from sources there are no conserved charges or symmetries in the Higgs phase; so the Higgs mechanism is the removal of symmetry from the theory. We show how physical features of defects, such as cosmic strings in the abelian Higgs model, are best understood in this context. Since there is a unique ground state, we address (ii) whether the path integral is a volume measure for the radial Higgs field $\mathcal{D}ρ\,ρ^{N-1}$ from the $N$ components of the Higgs multiplet, or a line measure $\mathcal{D}ρ$ as the $N-1$ would-be Goldstones can be removed in unitary gauge. We prove that the need to avoid quartic divergences demands a tower of counter terms that resum to exactly give the volume measure. So the size of the Hilbert space in the zero gauge coupling case and finite gauge coupling case are in one-to-one correspondence, despite the degeneracy of the ground state being lifted in the latter. As a cosmological application, we point out that the volume measure can make it exponentially more unlikely in $N(=4)$ for the Standard Model Higgs to relax to the electroweak vacuum in the early universe.

hep-th↗

arXiv2018

Constraints on Gravitation from Causality and Quantum Consistency

We examine the role of consistency with causality and quantum mechanics in determining the properties of gravitation. We begin by examining two different classes of interacting theories of massless spin 2 particles -- gravitons. One involves coupling the graviton with the lowest number of derivatives to matter, the other involves coupling the graviton with higher derivatives to matter, making use of the linearized Riemann tensor. The first class requires an infinite tower of terms for consistency, which is known to lead uniquely to general relativity. The second class only requires a finite number of terms for consistency, which appears as another class of theories of massless spin 2. We recap the causal consistency of general relativity and show how this fails in the second class for the special case of coupling to photons, exploiting related calculations in the literature. In a companion paper [1] this result is generalized to a much broader set of theories. Then, as a causal modification of general relativity, we add light scalar particles and recap the generic violation of universal free-fall they introduce and its quantum resolution. This leads to a discussion of a special type of scalar-tensor theory; the $F(\mathcal{R})$ models. We show that, unlike general relativity, these models do not possess the requisite counterterms to be consistent quantum effective field theories. Together this helps to remove some of the central assumptions made in deriving general relativity.

hep-th↗

arXiv2018

Dark Matter Axion Clump Resonance of Photons

Recently there has been interest in the physical properties of dark matter axion condensates. Due to gravitational attraction and self-interactions, they can organize into spatial localized clumps, whose properties were examined by us in Refs. [1, 2]. Since the axion condensate is coherently oscillating, it can conceivably lead to parametric resonance of photons, leading to exponential growth in photon occupancy number and subsequent radio wave emission. We show that while resonance always exists for spatially homogeneous condensates, its existence for a spatially localized clump condensate depends sensitively on the size of clump, strength of axion-photon coupling, and field amplitude. By decomposing the electromagnetic field into vector spherical harmonics, we are able to numerically compute the resonance from clumps for arbitrary parameters. We find that for spherically symmetric clumps, which are the true BEC ground states, the resonance is absent for conventional values of the QCD axion-photon coupling, but it is present for axions with moderately large couplings, or into hidden sector photons, or from scalar dark matter with repulsive interactions. We extend these results to non-spherically symmetric clumps, organized by finite angular momentum, and find that even QCD axion clumps with conventional couplings can undergo resonant decay for sufficiently large angular momentum. We discuss possible astrophysical consequences of these results, including the idea of a pile-up of clump masses and rapid electromagnetic emission in the sky from mergers.

hep-ph↗

arXiv2018

Scalar Dark Matter Clumps with Angular Momentum

The behavior of light scalar dark matter has been a subject of much interest recently as it can lead to interesting small scale behavior. In particular, this can lead to the formation of gravitationally bound clumps for these light scalars, including axions. In Ref. [1] we analyzed the behavior of these clumps, assuming spherical symmetry, allowing for both attractive and repulsive self-interactions. There is a maximum allowed mass for the clumps in the case of attractive interactions, and a minimum radius for the clumps in the case of repulsive interactions, which is saturated at large mass. Here we extend this work to include non-spherically symmetric clumps. Since the system tries to re-organize into a BEC ground state, we consider configurations with a conserved non-zero angular momentum, and construct minimum energy configurations at fixed particle number and fixed angular momentum. We find generalizations of the previous spherically symmetric results. In particular, while there is still a maximum mass for the attractive case, its value increases with angular momentum. Also, the minimum radius in the repulsive case is raised to higher radii. We clarify how a recent claim in the literature of an upper bound on angular momentum is due to inaccurate numerics. In a forthcoming paper we shall investigate the possibility of resonance of axion clumps into both visible and hidden sector photons, and analyze how the altered mass and radius from non-zero angular momentum affects the resonance.

hep-ph↗

arXiv2018

Can Light Dark Matter Solve the Core-Cusp Problem?

Recently there has been much interest in light dark matter, especially ultra-light axions, as they may provide a solution to the core-cusp problem at the center of galaxies. Since very light bosons can have a de Broglie wavelength that is of astrophysical size, they can smooth out the centers of galaxies to produce a core, as opposed to vanilla dark matter models, and so it has been suggested that this solves the core-cusp problem. In this work, we critically examine this claim. While an ultra-light particle will indeed lead to a core, we examine whether the relationship between the density of the core and its radius matches the data over a range of galaxies. We first review data that shows the core density of a galaxy $ρ_c$ varies as a function of the core radius $R_c$ as $ρ_c\propto1/R_c^β$ with $β\approx1$. We then compare this to theoretical models. We examine a large class of light scalar dark matter models, governed by some potential $V$. For simplicity, we take the scalar to be complex with a global $U(1)$ symmetry in order to readily organize solutions by a conserved particle number. However, we expect our central conclusions to persist even for a real scalar, and furthermore, a complex scalar matches the behavior of a real scalar in the non-relativistic limit, which is the standard regime of interest. For any potential $V$, we find the relationship between $ρ_c$ and $R_c$ for ground state solutions is always in one of the following regimes: (i) $β\gg1$, or (ii) $β\ll1$, or (iii) unstable, and so it never matches the data. We also find similar conclusions for virialized dark matter, more general scalar field theories, degenerate fermion dark matter, superfluid dark matter, and general polytropes. We conclude that the solution to the core-cusp problem is more likely due to either complicated baryonic effects or some other type of dark matter interactions.

astro-ph.CO↗

arXiv2018

Analysis of Dark Matter Axion Clumps with Spherical Symmetry

Recently there has been much interest in the spatial distribution of light scalar dark matter, especially axions, throughout the universe. When the local gravitational interactions between the scalar modes are sufficiently rapid, it can cause the field to re-organize into a BEC of gravitationally bound clumps. While these clumps are stable when only gravitation is included, the picture is complicated by the presence of the axion's attractive self-interactions, which can potentially cause the clumps to collapse. Here we perform a detailed stability analysis to determine under what conditions the clumps are stable. In this paper we focus on spherical configurations, leaving aspherical configurations for future work. We identify branches of clump solutions of the axion-gravity-self-interacting system and study their stability properties. We find that clumps that are (spatially) large are stable, while clumps that are (spatially) small are unstable and may collapse. Furthermore, there is a maximum number of particles that can be in a clump. We map out the full space of solutions, which includes quasi-stable axitons, and clarify how a recent claim in the literature of a new ultra-dense branch of stable solutions rests on an invalid use of the non-relativistic approximation. We also consider repulsive self-interactions that may arise from a generic scalar dark matter candidate, finding a single stable branch that extends to arbitrary particle number.

hep-ph↗