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The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational-wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational-wave observations by LISA to probe the universe.

The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of gravitational waves can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas.

We compute quantum corrections to the Raychaudhuri equation by replacing classical geodesies with quantal (Bohmian) trajectories and show that they prevent focusing of geodesies and the formation of conjugate points. We discuss implications for the Hawking-Penrose singularity theorems and curvature singularities. [ABSTRACT FROM AUTHOR]

The extremely small accelerations of objects required for the onset of modified Newtonian dynamics, or modified Newtonian dynamics (MOND), makes testing the hypothesis in conventional terrestrial labo-ratories virtually impossible. This is due to the large background acceleration of Earth, which is transmitted to the acceleration of test objects within an apparatus. We show, however, that it may be possible to test MOND-type hypotheses with experiments using a conventional apparatus capable of tracking very small accelerations of its components but performed in locally inertial frames such as artificial satellites and other freely falling laboratories. For example, experiments involving an optical interferometer or a torsion balance in these laboratories would show nonlinear dynamics and displacement amplitudes larger than expected. These experiments may also be able to test potential violations of the strong equivalence principle by MOND and to distinguish between its two possible interpretations (modified inertia and modified gravity). [ABSTRACT FROM AUTHOR]

Attempts to formulate a quantum theory of gravitation are collectively known as quantum gravity. Various approaches to quantum gravity such as string theory and loop quantum gravity, as well as black hole physics and doubly special relativity theories predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called generalized uncertainty principle (GUP). We have proposed a GUP consistent with string theory, black hole physics, and doubly special relativity theories and have showed that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it suggests that the space that confines it must be quantized, and in fact that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this may signal the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale. Because this influences all the quantum Hamiltonians in an universal way, it predicts quantum gravity corrections to various quantum phenomena. Therefore, in the present work we compute these corrections to the Lamb shift, simple harmonic oscillator, Landau levels, and the tunneling current in a scanning tunneling microscope. [ABSTRACT FROM AUTHOR]

We re-examine the fine-tuning problem of the Higgs mass, when an antisymmetric 2-form Kalb-Ramond (KR) field is present in the bulk of a Randall-Sundrum (RS) braneworld. Taking into account the back reaction of the KR field, we obtain the exact correction to the RS metric. The modified metric also warps the Higgs mass from Planck scale (in higher dimension) to TeV scale (on the visible brane) for a range of values of krexceeding the original RS value (where k= Planck mass and r= size of extra dimension). However, it requires an extraordinary suppression of the KR field density, indicating the re-appearence of the fine-tuning problem in a different guise. The new spacetime also generates a small negative cosmological constant on the visible brane. These results are particularly relevant for certain string-based models, where the KR field is unavoidably present in the bulk. We further show that such a bulk antisymmetric KR field fails to stabilize the braneworld.

The possibility that the asymptotic quasi-normal mode (QNM) frequencies can be used to obtain the Bekenstein-Hawking entropy for the Schwarzschild black hole-commonly referred to as Hod's conjecture-has received considerable attention. To test this conjecture, using the monodromy technique, attempts have been made to analytically compute the asymptotic frequencies for a large class of black hole spacetimes. In an earlier work, two of the current authors computed the high frequency QNMs for scalar perturbations of (D+ 2)-dimensional spherically symmetric, asymptotically flat, single horizon spacetimes with generic power-law singularities. In this work, we extend these results to asymptotically non-flat spacetimes. Unlike in the earlier analyses, we treat asymptotically flat and de Sitter spacetimes in a unified manner, while the asymptotic anti-de Sitter spacetimes are considered separately. We obtain master equations for the asymptotic QNM frequency for all three cases. We show that for all three cases, the real part of the asymptotic QNM frequency-in general-is not proportional to ln(3), thus indicating that Hod's conjecture may be restrictive.

We compute the high-frequency quasi-normal modes (QNM) for scalar perturbations of spherically symmetric single-horizon black holes in (D+ 2)-spacetime dimensions with generic curvature singularities and having metrics of the form ds2= ?xp(dy2? dx2) + xqd?2Dnear the singularity x= 0. The real part of the QN frequencies is shown to be proportional to log[1 + 2cos(?[qD? 2]/2)] where the constant of proportionality is equal to the Hawking temperature for non-degenerate black holes and inverse of the horizon radius for degenerate black holes. Apart from agreeing with the QN frequencies that have been computed earlier, our results imply that the horizon area spectrum for the general spherically symmetric black holes is equispaced. Applying our results, we also find the QNM frequencies for an extremal Reissner-Nordström and various stringy black holes.

The reduced phase space formalism for quantizing black holes has recently been extended to find the area and angular momentum spectra of four-dimensional Kerr black holes. We extend this further to rotating black holes in all spacetime dimensions and show that although as in four dimensions the spectrum is discrete, it is not equispaced in general. As a result, Hawking radiation spectra from these black holes are continuous, as opposed to the discrete spectrum predicted for four-dimensional black holes.

We review some recent advances in black-hole thermodynamics including statistical mechanical origins of black-hole entropy and its leading order corrections from the view points of various quantum gravity theories. We then examine the problem of information loss and some possible approaches to its resolution. Finally, we study some proposed experiments which may be able to provide experimental signatures of black holes.

The generalized uncertainty principle, motivated by string theory and non-commutative quantum mechanics, suggests significant modifications to the Hawking temperature and evaporation process of black holes. For extra-dimensional gravity with Planck scale O(TeV), this leads to important changes in the formation and detection of black holes at the large hadron collider. The number of particles produced in Hawking evaporation decreases substantially. The evaporation ends when the black-hole mass is Planck scale, leaving a remnant and a consequent missing energy of order TeV. Furthermore, the minimum energy for black-hole formation in collisions is increased, and could even be increased to such an extent that no black holes are formed at LHC energies.

Bekenstein proposed that the spectrum of horizon area of quantized black holes must be discrete and uniformly spaced. We examine this proposal in the context of spherically symmetric charged black holes in a general class of gravity theories. By imposing suitable boundary conditions on the reduced phase space of the theory to incorporate the thermodynamic properties of these black holes and then performing a simplifying canonical transformation, we are able to quantize the system exactly. The resulting spectra of horizon area, as well as that of charge are indeed discrete. Within this quantization scheme, near-extremal black holes (of any mass) turn out to be highly quantum objects, whereas extremal black holes do not appear in the spectrum, a result that is consistent with the postulated third law of black hole thermodynamics.

We quantize the spherically symmetric sector of generic charged black holes. Thermal properties are incorporated by imposing periodicity in Euclidean time, with period equal to the inverse Hawking temperature of the black hole. This leads to an exact quantization of the area (A) and charge (Q) operators. For the Reissner–Nordström black hole, A=4πGℏ(2n+p+1) and Q=me, for integers n,p,m. Consistency requires the fine structure constant to be quantized: e2/ℏ=p/m2. Remarkably, vacuum fluctuations exclude extremal black holes from the spectrum, while near extremal black holes are highly quantum objects. We also prove that horizon area is an adiabatic invariant.

We study quantum gravity effects on the density of states in statistical mechanics and its implications for the critical temperature of a Bose Einstein condensate and fraction of bosons in its ground state. We also study the effects of compact extra dimensions on the critical temperature and the fraction. We consider both neutral and charged bosons in the study and show that the effects may just be measurable in current and future experiments. [ABSTRACT FROM AUTHOR]

Planckian scattering of particles with angular momenta is studied by describing them as sources of the Kerr metric. In the shock wave formalism, it is found that the angular momenta do not contribute to the scattering amplitude in the eikonal limit. This is confirmed by using the wave equation of the test particle in the Kerr background.

We discuss an approach to compute two-particle scattering amplitudes for spinless light particles colliding at Planckian centre-of-mass energies, with increasing momentum transfer away from the eikonal limit. The leading corrections to the eikonal amplitude, in our ‘external metric’ approach, are shown to be vanishingly small in the limit of the source particle mass going to zero. For massless charged particles, the electromagnetic and gravitational interactions decouple in the eikonal limit, but mix non-trivially for the leading order corrections.

We derive loop quantum gravity corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole and near the classical singularity. We show that the resulting effective equation implies defocusing of geodesics due to the appearance of repulsive terms. This prevents the formation of conjugate points, renders the singularity theorems inapplicable, and leads to the resolution of the singularity for this spacetime. [ABSTRACT FROM AUTHOR]

We compute the quantum circuit complexity of the evolution of scalar curvature perturbations on expanding backgrounds, using the language of squeezed vacuum states. In particular, we construct a simple cosmological model consisting of an early-time period of de Sitter expansion followed by a radiation-dominated era and track the evolution of complexity throughout this history. During early-time de Sitter expansion the complexity grows linearly with the number of e-folds for modes outside the horizon. The evolution of complexity also suggests that the Universe behaves like a chaotic system during this era, for which we propose a scrambling time and Lyapunov exponent. During the radiation-dominated era, however, the complexity decreases until it "freezes in" after horizon reentry, leading to a "decomplexification" of the Universe. [ABSTRACT FROM AUTHOR]

In order for spacetimes with static extra dimensions to have four-dimensional de Sitter expansion they must have at least positive curvature, warping sourced by the four-dimensional expansion, or violate the null energy condition everywhere in the extra dimensions. We show how this constraint arises from the null Raychaudhuri equation, and that it is independent of the matter content, the Einstein equations, and is true point by point in the extra dimensions (not integrated), setting it apart from other no-go theorems in the literature. We present two previously known examples--a Freund-Rubin compactification with bulk cosmological constant, and a Randall-Sundrum model where the mismatch between the brane and bulk cosmological constants sources nontrivial warping--which evade the constraint and discuss the implications for flux compactifications. We also show that any spacetime with static compact extra dimensions and four-dimensional de Sitter expansion has an apparent horizon and antitrapped region in the extra dimensions, which may have interesting implications for the dynamics of bulk fields in cosmology. [ABSTRACT FROM AUTHOR]

The generalized uncertainty principle (GUP) is a modification of Heisenberg's Principle predicted by several theories of quantum gravity. It consists of a modified commutator between the position and momentum. In this work, we compute potentially observable effects that GUP implies for the harmonic oscillator, coherent, and squeezed states in quantum mechanics. In particular, we rigorously analyze the GUP-perturbed harmonic oscillator Hamiltonian, defining new operators that act as ladder operators on the perturbed states. We use these operators to define the new coherent and squeezed states. We comment on potential applications. [ABSTRACT FROM AUTHOR]

The unification of quantum mechanics and gravity remains as one of the primary challenges of present-day physics. Quantum-gravity-inspired phenomenological models offer a window to explore potential aspects of quantum gravity including qualitatively new behavior that can be experimentally tested. One such phenomenological model is the generalized uncertainty principle, which predicts a modified Heisenberg uncertainty relation and a deformed canonical commutator. It was recently shown that optomechanical systems offer significant promise to put stringent experimental bounds on such models. In this paper, we introduce a scheme to increase the sensitivity of these experiments with an extended sequence of pulsed optomechanical interactions. We also analyze the effects of optical phase noise and optical loss and present a strategy to mitigate such deleterious effects. [ABSTRACT FROM AUTHOR]

We derive the Hawking radiation spectrum of anyons, namely particles in (2+1)--dimension obeying fractional statistics, from a Bañados, Teitelboim, and Zanelli (BTZ) black hole, in the tunneling formalism. We examine ways of measuring the spectrum in experimentally realizable systems in the laboratory. [ABSTRACT FROM AUTHOR]

In general relativity, gravity is universally attractive, a feature embodied by the Raychaudhuri equation which requires that the expansion of a congruence of geodesics is always non-increasing, as long as matter obeys the strong or weak energy conditions. This behavior of geodesics is an important ingredient in general proofs of singularity theorems, which show that many spacetimes are singular in the sense of being geodesically incomplete and suggest that general relativity is itself incomplete. It is possible that alternative theories of gravity, which reduce to general relativity in some limit, can resolve these singularities, so it is of interest to consider how the behavior of geodesics is modified in these frameworks. We compute the leading corrections to the Raychaudhuri equation for the expansion due to models in string theory, braneworld gravity, f(R) theories, and loop quantum cosmology, for cosmological and black hole backgrounds, and show that while in most cases geodesic convergence is reinforced, in a few cases terms representing repulsion arise, weakening geodesic convergence and thereby the conclusions of the singularity theorems. [ABSTRACT FROM AUTHOR]

We address the validity of the formalism and results presented in S. Das, Phys. Rev. D 89, 084068 (2014) with regard to the quantum Raychaudhuri equation. The author obtained the so-called quantum Raychaudhuri equation by replacing classical geodesics with quantal trajectories arising from Bhommian mechanics. The resulting modified equation was used to draw some conclusions about the inevitability of focusing and the formation of conjugate points and therefore singularity. We show that the whole procedure is full of problematic points, on both physical relevancy and mathematical correctness. In particular, we illustrate the problems associated with the technical derivation of the so-called quantum Raychaudhuri equation, as well as its invalid physical implications. [ABSTRACT FROM AUTHOR]