trans-Planckian Regime Research Articles

The Asymptotically Safe Standard Model: From quantum gravity to dynamical chiral symmetry breaking

We present a comprehensive non-perturbative study of the phase structure of the asymptotically safe Standard Model. The physics scales included range from the asymptotically safe trans-Planckian regime in the ultraviolet, the intermediate high-energy regime with electroweak symmetry breaking to strongly correlated QCD in the infrared. All flows are computed with a self-consistent functional renormalisation group approach, using a vertex expansion in the fluctuation fields. In particular, this approach takes care of all physical threshold effects and the respective decoupling of ultraviolet degrees of freedom. Standard Model and gravity couplings and masses are fixed by their experimental low energy values. Importantly, we accommodate for the difference between the top pole mass and its Euclidean analogue. Both, the correct mass determination and the threshold effects have a significant impact on the qualitative properties, and in particular on the stability properties of the specific ultraviolet-infrared trajectory with experimental Standard Model physics in the infrared. We show that in the present rather advanced approximation the matter part of the asymptotically safe Standard Model has the same number of relevant parameters as the Standard Model, and is asymptotically free. This result is based on the novel UV fixed point found in the present work: the fixed point Higgs potential is flat but has two relevant directions. These results and their analysis are accompanied by a thorough discussion of the systematic error of the present truncation, also important for systematic improvements.

Unattainability of the trans-Planckian regime in nonlocal quantum gravity

Based on the ultraviolet asymptotic freedom of nonlocal quantum gravity, we show that the trans-Planckian energy regime is unattainable in laboratory experiments. As physical implications, it turns out that the violation of causality, typical of nonlocal field theories, can never be detected in particle accelerators, while the asymptotic freedom of the theory provides an elegant solution to the so called trans-Planckian cosmological problem.

Predictive power of grand unification from quantum gravity

If a grand-unified extension of the asymptotically safe Reuter fixed-point for quantum gravity exists, it determines free parameters of the grand-unified scalar potential. All quartic couplings take their fixed-point values in the trans-Planckian regime. They are irrelevant parameters that are, in principle, computable for a given particle content of the grand unified model. In turn, the direction of spontaneous breaking of the grand-unified gauge symmetry becomes predictable. For the flow of the couplings below the Planck mass, gauge and Yukawa interactions compete for the determination of the minimum of the effective potential.

Cosmology of the Symmetrical Relativity versus Spontaneous Creation of the Universe Ex Nihilo

The cosmology of "Spontaneous Creation of the Universe Ex Nihilo" and the cosmology of the Symmetrical Relativity offer proposals to explain the creation and evolution of the universe. In essence they are still very distinct. However, we will argue that there was an antecedent to the big bang. Thus, we will penetrate a trans-Planckian regime, where we find an effective Planck length $L_P^{\prime}\rightarrow 0$. This will lead to more fundamental physical reflections about {\it nothing} in the cosmology of spontaneous creation. From the point of view of spontaneous creation, the step backwards went back to another principle, based on the {\it information}, which led to the big bang. While the spontaneous creation refers to the virtual pre-existence of {\it information}, which would have emerged randomly from {\it nothing}, the cosmology of Symmetrical Relativity does not stop there: we go back to one's own origin by projecting it before the creation of one's own time. From the present perspective, {\it nothing} is a primordial vacuum, whose {\it information} has made the universe by condensing and igniting. It was not randomly created, since the entropy had to vary from infinite (chaos) to zero (big bang) by violating the 2nd.law of thermodynamics in a trans-Planckian regime. {\it Nothing} or chaos with infinite entropy precedes the big bang (null entropy) within a trans-Planckian scenario and it determines the whole plot until the total extinction of the universe. We will show that {\it information}, besides not being born of the universe, also does not develop from it like the computational idea of Artificial Intelligence (AI). Thus, the universe is not simply self-taught as defended by the spontaneous creation. This could shed light on the problem of Penrose's Weyl curvature hypothesis, which considers a null Weyl curvature due to a null entropy in the big bang.

Consistent early and late time cosmology from the RG flow of gravity

We investigate the compatibility of cosmological constraints on inflation and the cosmological constant with the asymptotic safety scenario of quantum gravity. The effective action is taken to be of f(R) form, truncated to second order. The flow generated by the Functional Renormalisation Group Equation is analysed and it is found to allow for trajectories that are compatible with the observational constraints on the parameters of the action, both at early and late cosmological times. In particular, the gravitational effective dynamics generated in the trans-Planckian regime flows to Starobinsky inflation at early times and to standard Einstein Gravity with a cosmological constant at late times. Moreover, the cosmological constant acquires an energy dependence at 10−2 eV, increasing from its current value of 10−66 eV2 on Hubble scale to a value of 1030 eV2 at inflation scale.

Quantum-gravity predictions for the fine-structure constant

Asymptotically safe quantum fluctuations of gravity can uniquely determine the value of the gauge coupling for a large class of grand unified models. In turn, this makes the electromagnetic fine-structure constant calculable. The balance of gravity and matter fluctuations results in a fixed point for the running of the gauge coupling. It is approached as the momentum scale is lowered in the transplanckian regime, leading to a uniquely predicted value of the gauge coupling at the Planck scale. The precise value of the predicted fine-structure constant depends on the matter content of the grand unified model. It is proportional to the gravitational fluctuation effects for which computational uncertainties remain to be settled.

Bouncing and emergent cosmologies from Arnowitt–Deser–Misner RG flows

Asymptotically safe gravity provides a framework for the description of gravity from the trans-Planckian regime to cosmological scales. According to this scenario, the cosmological constant and Newton’s coupling are functions of the energy scale whose evolution is dictated by the renormalization group (RG) equations. The formulation of the RG equations on foliated spacetimes, based on the Arnowitt–Deser–Misner (ADM) formalism, furnishes a natural way to construct the RG energy scale from the spectrum of the Laplacian operator on the spatial slices. Combining this idea with an RG improvement procedure, in this work we study quantum gravitational corrections to the Einstein–Hilbert action on Friedmann–Lemaître–Robertson–Walker backgrounds. The resulting quantum-corrected Friedmann equations can give rise to both bouncing cosmologies and emergent Universe solutions. Our bouncing models do not require the presence of exotic matter and emergent Universe solutions can be constructed for any allowed topology of the spatial slices.

Top mass from asymptotic safety

We discover that asymptotically safe quantum gravity could predict the top-quark mass. For a broad range of microscopic gravitational couplings, quantum gravity could provide an ultraviolet completion for the Standard Model by triggering asymptotic freedom in the gauge couplings and bottom Yukawa and asymptotic safety in the top-Yukawa and Higgs-quartic coupling. We find that in a part of this range, a difference of the top and bottom mass of approximately 170GeV is generated and the Higgs mass is determined in terms of the top mass. Assuming no new physics below the Planck scale, we construct explicit Renormalization Group trajectories for Standard Model and gravitational couplings which link the transplanckian regime to the electroweak scale and yield a top pole mass of Mt,pole≈171GeV.

Reheating the Universe at Criticality

We present the general discussion on the inflection point inflation with small or large inflaton fields and show the effects of reheating dynamics on the inflationary predictions. In order to compare the model predictions with precisely measured CMB anisotropies and constrain the inflation models, the knowledge of the reheating dynamics is required. Inflection point inflation extended to the trans-Planckian regime can accommodate a sizable tensor-to-scalar ratio at the detectable level in the future CMB experiments.

A note on trans-Planckian tail effects

We study the proposal by Mersini et al. [1] that the observed dark energy might be explained by the back-reaction of the set of tail modes in a theory with a dispersion relation in which the mode frequency decays exponentially in the trans-Planckian regime. The matter tail modes are frozen out, however they induce metric fluctuations. The energy-momentum tensor with which the tail modes effect the background geometry obtains contributions from both metric and matter fluctuations. We calculate the equation of state induced by the tail modes taking into account the gravitational contribution. We find that, in contrast to the case of frozen super-Hubble cosmological fluctuations, in this case the matter perturbations dominate, and they yield an equation of state which to leading order takes the form of a positive cosmological constant.

A note on trans-Planckian tail effects

We study the proposal by Mersini et al. [1] that the observed dark energy might be explained by the back-reaction of the set of tail modes in a theory with a dispersion relation in which the mode frequency decays exponentially in the trans-Planckian regime. The matter tail modes are frozen out, however they induce metric fluctuations. The energy-momentum tensor with which the tail modes effect the background geometry obtains contributions from both metric and matter fluctuations. We calculate the equation of state induced by the tail modes taking into account the gravitational contribution. We find that, in contrast to the case of frozen super-Hubble cosmological fluctuations, in this case the matter perturbations dominate, and they yield an equation of state which to leading order takes the form of a positive cosmological constant.

Lorentz invariance without trans-Planckian physics?

We explore the possibility that, in a quantum field theory with Planck scale cutoff Λ≃mp, observable quantities for low-energy processes respect the Lorentz symmetry. In particular, we compute the one-loop radiative correction Π to the self-energy of a scalar field with λϕ4 interaction, using a modified (non-invariant) propagator which vanishes in the trans-Planckian regime, as expected in the “classicalisation” scenario. We then show that, by imposing the result does not depend on Λ (in the limit Λ→mp), an explicit (albeit not unique) expression for Π can be derived, which is similar to the one simply obtained with the standard Feynman propagator and a cutoff Λ=mp.

Self-sustained wormholes in modified dispersion relations

In this work, we consider the possibility that wormhole geometries are sustained by their own quantum fluctuations, in the context of modified dispersion relations. More specifically, the energy density of the graviton one-loop contribution to a classical energy in a wormhole background is considered as a self-consistent source for wormholes. In this semi-classical context, we consider specific choices for the Rainbow's functions and find solutions for wormhole geometries in the cis-planckian and trans-planckian regimes. In the former regime, the wormhole spacetimes are not asymptotically flat and need to be matched to an exterior vacuum solution. In the latter trans-planckian regime, we find that the quantum corrections are exponentially suppressed, which provide asymptotically flat wormhole geometries with a constant shape function, i.e., b(r)=r_t, where r_t is the wormhole throat. In addition to this analysis, we also fix the geometry by considering the behaviour of a specific shape function through a variational approach which imposes a local analysis to the problem at the wormhole throat. We further explore the respective parameter range of the Rainbow's functions, and find a good agreement with previous work.

Regular black holes in UV self-complete quantum gravity

In this Letter we investigate the role of regular (curvature singularity-free) black holes in the framework of UV self-complete quantum gravity. The existence of a minimal length, shielding the trans-Planckian regime to any physical probe, is self-consistently included into the black hole probe itself. In this way we obtain to slightly shift the barrier below the Planck length, with the UV self-complete scenario self-consistently confirmed.

Relic dark energy from the trans-Planckian regime

As yet, there is no underlying fundamental theory for the trans-Planckian regime. There is a need to address the issue of how the observables in our present Universe are affected by processes that may have occurred at super-Planckian energies (referred to as the trans-Planckian regime). Specifically, we focus on the impact the trans-Planckian regime has on two observables: namely, dark energy and the cosmic microwave background radiation (CMBR) spectrum. We model the trans-Planckian regime by introducing a 1-parameter family of smooth non-linear dispersion relations which modify the frequencies at very short distances. A particular feature of the family of dispersion functions chosen is the production of ultralow frequencies at very high momenta k (for $k>{M}_{P}).$ We name the range of the ultralow energy modes (of very short distances) that have frequencies equal to or less than the current Hubble rate ${H}_{0}$ as the tail modes. These modes are still frozen today due to the expansion of the Universe. We calculate their energy today and show that the tail provides a strong candidate for the dark energy of the Universe. During inflation, their energy is about 122 to 123 orders of magnitude smaller than the total energy, for any random value of the free parameter in the family of dispersion relations. For this family of dispersions, we present the exact solutions and show that the CMBR spectrum is that of a (nearly) blackbody, and that the adiabatic vacuum is the only choice for the initial conditions.

Relic dark energy from the trans-Planckian regime

Relic dark energy from the trans-Planckian regime