Semiclassical Theory Of Gravity Research Articles

Time–Energy Uncertainty Relation for Neutrino Oscillations: Historical Development, Applications, and Future Prospects

The time–energy uncertainty relation (TEUR) plays a fundamental role in quantum mechanics, as it allows the grasping of peculiar aspects of a variety of phenomena based on very general principles and symmetries of the theory. Using the Mandelstam–Tamm method, TEUR has recently been derived for neutrino oscillations by connecting the uncertainty in neutrino energy with the characteristic timescale of oscillations. Interestingly, the suggested interpretation of neutrinos as unstable-like particles has proved to naturally emerge in this context. Further aspects were later discussed in semiclassical gravity theory, by computing corrections to the neutrino energy uncertainty in a generic stationary curved spacetime, and in quantum field theory, where the clock observable turns out to be identified with the non-conserved flavor charge operator. In the present work, we give an overview on the above achievements. In particular, we analyze the implications of TEUR and explore the impact of gravitational and non-relativistic effects on the standard condition for neutrino oscillations.

Semiclassical 3D gravity as an average of large-c CFTs

A two-dimensional CFT dual to a semiclassical theory of gravity in three dimensions must have a large central charge c and a sparse low energy spectrum. This constrains the OPE coefficients and density of states of the CFT via the conformal bootstrap. We define an ensemble of CFT data by averaging over OPE coefficients subject to these bootstrap constraints, and show that calculations in this ensemble reproduce semiclassical 3D gravity. We analyze a wide variety of gravitational solutions, both in pure Einstein gravity and gravity coupled to massive point particles, including Euclidean wormholes with multiple boundaries and higher topology spacetimes with a single boundary. In all cases we find that the on-shell action of gravity agrees with the ensemble-averaged CFT at large c. The one-loop corrections also match in the cases where they have been computed. We also show that the bulk effective theory has random couplings induced by wormholes, providing a controlled, semiclassical realization of the mechanism of Coleman, Giddings, and Strominger.

Validity of semiclassical limit to quantum gravity in two-mode oscillating quantized massive scalar field quantum cosmology

Semiclassical Einstein equations are used to describe the interaction of the back-reaction of the classical gravitational field with quantum matter fields in semiclassical gravity. We in our previous studies have made use of the semiclassical approximation to demonstrate the phenomenon of particle production, often called preheating/reheating of the universe, which occurs after the inflationary epoch during the oscillatory phase of two-mode quantized scalar field of chaotic inflationary model. During this oscillatory phase, back-reaction effects from the created particles, on account of the quantum nature of the states considered, could be significant and one might be concerned about the validity of the semiclassical approximation in these two-mode quantum optical states. The validity of the semiclassical approximation in these states is examined and it is presented how the magnitude of states parameter draws limit on the applicability and reliability of semiclassical theory of gravity. It is argued that semiclassical theory to gravity is a good approximation for states which are closer to coherent states i.e., with coherent parameters greater than unity and with squeezed parameter much smaller than unity.

Ultra-compact objects from semi-classical gravity

In a recent report, Carballo-Rubio [1] utilizes the semi-classical theory of gravity to obtain a generalized Tolman-Oppenheimer-Volkoff (TOV) equation. This model has a new coupling constant $l_p$ implying two different modified TOV equation forms characterized by the sign of $p'$. The negative branch reduces to the ordinary GR-TOV in the limit of $l_p\to0$, while the positive one does not. In the positive branch, Carballo-Rubio was able to find the exact solutions using the constant-$\lambda$ trick. In this work, we investigate whether this theory's negative branch can also provide a different feature of the ultra-compact object compared to those obtained from the GR-TOV equation. We study ultra-compact objects with an isotropically ideal fluid matter where we use a simple but physically motivated equation of state $\rho=p/w+\rho_0$ with $w$=1 and $w$=1/3. In general, we obtain that the range of $l_p$ is very restricted and must not be equal to $r_c$. Here $r_c$ is the starting point of integration located at the center of the star. While $l_p$ should be set to be much larger than Planck length $L_\text{Pl}$. Consequently, the mass-radius curves for the various value of $l_p$ for both $w$ cases are still indistinguishable from the standard GR-TOV results. Hence from the negative branch of $p'(r)$, the additional free parameter $l_p$ does not provide a significant effect compared to the standard GR-TOV equation results, even though $l_p$ is not in the limit of $l_p\to0$ anymore. Therefore, similar to the conclusion in Ref. [3] with GR theory that the ultra-compact objects from negative branch of semi-classical gravity with a linear equation of state are unable to generate demanding gravitational echoes.

Laws of black hole thermodynamics in semiclassical gravity

The first and second laws of black hole thermodynamics are verified to emerge from a generic semiclassical theory of gravity for which a Hamiltonian formulation can be defined. The first law is established in stationary spacetimes, and the second law is established in the here defined ‘piecewise stationary’ spacetimes. Black hole entropy is defined in the Noether charge approach, and the entropy for the matter in its exterior is the von Neumann entropy of the quantum fields. These results strongly support the interpretation of black hole entropy as an account of the information that is hidden behind the horizon.

Density fluctuations and single-mode thermal states in the FRW universe

Using single-mode squeezed and coherent thermal states formalism, we analyzed the validity of the semiclassical Einstein equation (SCEE) in the flat Friedmann–Robertson–Walker universe by analyzing the density fluctuations in terms of a massive inflaton. In a single-mode squeezed thermal states the density fluctuations are too large; consequently, the semiclassical theory of gravity (SCTG) does not hold good, for squeezing parameter greater than unity, i.e., $$r_{s}>1$$; however, the theory is valid when this related squeezing parameter is smaller than the unity, i.e., $$r_{s}<<1$$ and $$r_{s}<1$$. Also, it is noted that the SCEE is dependable on coherent thermal state formalism. The current study provides a description of the density fluctuations as a result of the quantum and thermal effects in the SCTG.

Oscillating inflaton power-law cosmology in two-mode quantum optical states

In this paper, we study the semiclassical evolution of a “coherently oscillating massive scalar field”. This field is nominally linked to the spatially levelled Friedmann–Robertson–Walker (FRW) metric. By use of two-mode quantum optical states formalism, we evaluated the power-law cosmology with scale factor as a power function of cosmic time. In the oscillatory phase of scalar field, it was found that, in all the four different combinations of quantum states, quantum scalar field obeying the time-dependent Schrödinger equation leads to the power-law expansion, in good agreement with that of the matter-dominated era. However, in the semiclassical theory of gravity in contrary to the classical description of gravity, we obtained two behavioral solutions corresponding to two different pattern evolution of the scale factor. This behavioral pattern evolution of scale factor of the universe has an important quantum implication associated with it.

Generally covariant dynamical reduction models and the Hadamard condition

We provide general guidelines for generalizing dynamical reduction models to curved spacetimes and propose a class of generally covariant relativistic versions of the Ghirardi-Rimini-Weber model. We anticipate that the collapse operators of our class of models may play a role in a yet-to-be-formulated theory of semiclassical gravity with collapses. We show explicitly that the collapse operators map a dense domain of states that are initially Hadamard to final Hadamard states---a property that we expect will be needed for the construction of such a semiclassical theory. Finally, we provide a simple example in which we explicitly compute the violations in energy-momentum due to the state reduction process and conclude that this violation is of the order of a parameter of the model---supposed to be small.

Effects of Newtonian gravitational self-interaction in harmonically trapped quantum systems.

The Schrödinger–Newton equation has gained attention in the recent past as a nonlinear modification of the Schrödinger equation due to a gravitational self-interaction. Such a modification is expected from a fundamentally semi-classical theory of gravity and can, therefore, be considered a test case for the necessity of the quantisation of the gravitational field. Here we provide a thorough study of the effects of the Schrödinger–Newton equation for a micron-sized sphere trapped in a harmonic oscillator potential. We discuss both the effect on the energy eigenstates and the dynamical behaviour of squeezed states, covering the experimentally relevant parameter regimes.

Hadron Physics from Superconformal Quantum Mechanics and Its Light-Front Holographic Embedding

The complex nonperturbative color-confining dynamics of QCD is well captured in a semiclassical effective theory based on superconformal quantum mechanics and its extension to the light-front. I describe here how this new approach to hadron physics incorporates confinement, the appearance of nearly massless pseudoscalar particles, and Regge spectroscopy consistent with experiment. It also gives remarkable connections between the meson and baryon spectrum across the light and heavy-light hadron spectrum. I also briefly discuss how higher spin states are consistently described in this framework by the holographic embedding of the superconformal theory in a higher dimensional semiclassical gravity theory.

Emergent gravitational dynamics in a relativistic Bose-Einstein condensate

Analogue models of gravity have played a pivotal role in the past years by providing a test bench for many open issues in quantum field theory in curved spacetime such as the robustness of Hawking radiation and cosmological particle production. More recently, the same models have offered a valuable framework within which current ideas about the emergence of spacetime and its dynamics could be discussed via convenient toy models. In this context, we study here an analogue gravity system based on a relativistic Bose--Einstein condensate. We show that in a suitable limit this system provides not only an example of an emergent spacetime (with a massive and a massless relativistic fields propagating on it) but also that such spacetime is governed by an equation with geometric meaning that takes the familiar form of Nordstr{\"o}m theory of gravitation. In this equation the gravitational field is sourced by the expectation value of the trace of the effective stress energy tensor of the quasiparticles while the Newton and cosmological constants are functions of the fundamental scales of the microscopic system. This is the first example of analogue gravity in which a Lorentz invariant, geometric theory of semiclassical gravity emerges from an underlying quantum theory of matter in flat spacetime.

The Schrödinger–Newton equation and its foundations

The necessity of quantising the gravitational field is still subject to an open debate. In this paper we compare the approach of quantum gravity, with that of a fundamentally semi-classical theory of gravity, in the weak-field non-relativistic limit. We show that, while in the former case the Schrödinger equation stays linear, in the latter case one ends up with the so-called Schrödinger–Newton equation, which involves a nonlinear, non-local gravitational contribution. We further discuss that the Schrödinger–Newton equation does not describe the collapse of the wave-function, although it was initially proposed for exactly this purpose. Together with the standard collapse postulate, fundamentally semi-classical gravity gives rise to superluminal signalling. A consistent fundamentally semi-classical theory of gravity can therefore only be achieved together with a suitable prescription of the wave-function collapse. We further discuss, how collapse models avoid such superluminal signalling and compare the nonlinearities appearing in these models with those in the Schrödinger–Newton equation.

Gravitational decoherence, alternative quantum theories and semiclassical gravity

In this report we discuss three aspects: 1) Semiclassical gravity theory (SCG): 4 levels of theories describing the interaction of quantum matter with classical gravity. 2) Alternative Quantum Theories: Discerning those which are derivable from general relativity (GR) plus quantum field theory (QFT) from those which are not 3) Gravitational Decoherence: derivation of a master equation and examination of the assumptions which led to the claims of observational possibilities. We list three sets of corresponding problems worthy of pursuit: a) Newton-Schrödinger Equations in relation to SCG; b) Master equation of gravity-induced effects serving as discriminator of 2); and c) Role of gravity in macroscopic quantum phenomena.

Newtonian semiclassical gravity in the Ghirardi–Rimini–Weber theory with matter density ontology

We propose a Newtonian semiclassical gravity theory based on the GRW collapse theory with matter density ontology (GRWm), which we term GRWmN. The theory is proposed because, as we show, the standard Newtonian semiclassical gravity theory based on the Schroedinger-Newton equations does not have a consistent Born rule probability interpretation for gravitationally self-interacting particles and implies gravitational cat states for macroscopic mass superpositions. By contrast, we show that GRWmN has a consistent statistical description of gravitationally self-interacting particles and adequately suppresses the cat states for macroscopic superpositions. Two possible routes to experimentally testing GRWmN are also considered. We conclude with a discussion of possible variants of GRWmN, what a general relativistic extension would involve, and various objections that might be raised against semiclassical gravity theories like GRWmN.

Might Quantum-Induced Deviations from the Einstein Equations Detectably Affect Gravitational Wave Propagation?

A quantum measurement-like event can produce any of a number of macroscopically distinct results, with corresponding macroscopically distinct gravitational fields, from the same initial state. Hence the probabilistically evolving large-scale structure of space-time is not precisely or even always approximately described by the deterministic Einstein equations. Since the standard treatment of gravitational wave propagation assumes the validity of the Einstein equations, it is questionable whether we should expect all its predictions to be empirically verified. In particular, one might expect the stochasticity of amplified quantum indeterminacy to cause coherent gravitational wave signals to decay faster than standard predictions suggest. This need not imply that the radiated energy flux from gravitational wave sources differs from standard theoretical predictions. An underappreciated bonus of gravitational wave astronomy is that either detecting or failing to detect predicted gravitational wave signals would constrain the form of the semi-classical theory of gravity that we presently lack.

Quantum modifications to gravity waves in de Sitter spacetime

We treat a model in which tensor perturbations of de Sitter spacetime, represented as a spatially flat model, are modified by the effects of the vacuum fluctuations of a massless conformally invariant field, such as the electromagnetic field. We use the semiclassical theory of gravity with the expectation value of the conformal field stress tensor as a source. We first study the stability of de Sitter spacetime by searching for growing, spatially homogeneous modes, and conclude that it is stable within the limits of validity of the semiclassical theory. We next examine the modification of linearized plane gravity waves by the effects of the quantum stress tensor. We find a correction term which is of the same form as the original wave, but displaced in phase by $\ensuremath{\pi}/2$, and with an amplitude which depends upon an initial time. The magnitude of this effect is proportional to the change in scale factor after this time. We discuss alternative interpretations of this time, but pay particular attention to the view that this is the beginning of inflation. So long as the energy scale of inflation and the proper frequency of the mode at the beginning of inflation are well below the Planck scale, the fractional correction is small. However, modes which are trans-Planckian at the onset of inflation can undergo a significant correction. The increase in amplitude can potentially have observable consequences through a modification of the power spectrum of tensor perturbations in inflationary cosmology. This enhancement of the power spectrum depends upon the initial time, and is greater for shorter wavelengths.

OSCILLATORY PHASE OF NONCLASSICAL THERMAL INFLATON IN FRW UNIVERSE

A minimally coupled nonclassical homogeneous scalar field is examined in the flat FRW universe in the semiclassical theory of gravity. Particle production in thermal coherent and squeezed states is studied for the flat FRW universe, in the oscillatory phase of the inflaton. Solutions for the semiclassical Friedmann equations are obtained in the thermal nonclassical states. Validity of the semiclassical theory is examined in the thermal coherent and squeezed states in the oscillatory phase of inflaton. Particle creation can be enhanced due to thermal and quantum effects. Quantum fluctuations of the inflaton in thermal coherent and squeezed state formalisms are also studied. Classical gravity differ from semiclassical gravity in the thermal coherent state only by an amplitude factor.

NONCLASSICAL SCALAR FIELD IN THE FRW UNIVERSE

Nonclassical representation of a minimally coupled scalar field in the open and closed FRW universe, is studied in the semiclassical theory of gravity. Particle production of a nonclassical scalar field in the coherent and squeezed state formalisms in the open FRW universe is examined. Numerical solutions to the semiclassical Friedmann equations are obtained for both the closed and open models in the coherent and squeezed state formalisms. Mandel's Q parameter of the quantum optics is studied in the cosmological context with associated cosmological parameters, in the semiclassical theory of gravity.

DENSITY FLUCTUATIONS IN THE OSCILLATORY PHASE OF A NONCLASSICAL INFLATON IN THE FRW UNIVERSE

The use of the coherent and squeezed state formalisms of quantum optics for a minimally coupled nonclassical inflaton in the FRW metric is studied, in the semiclassical theory of gravity. The leading order solutions to the semiclassical Einstein equations in the coherent, squeezed and squeezed vacuum states are obtained perturbatively and exhibit power law expansion behavior. The validity of the semiclassical theory is examined in the squeezed vacuum state in the oscillatory phase of the inflaton. The semiclassical theory in the oscillatory phase of the nonclassical inflaton holds only if the associated squeezing parameter is much smaller than unity. Quantum fluctuations of the inflaton are also examined in the coherent and squeezed state formalisms.

Particle Creation in Anisotropically Expanding Universe

Using squeezed vacuum states formalism of quantum optics, a homogeneous and massive scalar field minimally coupled to gravity in Bianchi type-I model of the universe is examined in the frame work of semiclassical theory of gravity. Hence an approximate leading solution to the semiclassical Einstein equation is found. The next order solution for each scale factor in their respective direction show power law of expansion. It is further noted that evolution of scale factors are mutually correlated. The phenomena of nonclassical particle creation is also examined in the anisotropic background cosmology.