Small Vacuum Energy Research Articles

The elastic vacuum

The quantum gravity vacuum must contain virtual fluctuations of black hole microstates. These extended-sized fluctuations get “crushed” when a closed trapped surface forms, and turn into on-shell “fuzzball” states that resolve the information puzzle. We argue that these same fluctuations can get “stretched” by the anti-trapped surfaces in an expanding cosmology, and that this stretching generates vacuum energy. The stretching happens when the Hubble deceleration reduces quickly, which happens whenever the pressure drops quickly. We thus get an inflation-scale vacuum energy when the heavy GUTS particles become nonrelativistic, and again a small vacuum energy when the radiation phase turns to dust. The expansion law in the radiation phase does not allow stretching, in agreement with the observed irrelevance of vacuum energy in that phase.

Testing swampland conjectures with machine learning

We consider Type IIB compactifications on an isotropic torus T^6 threaded by geometric and non geometric fluxes. For this particular setup we apply supervised machine learning techniques, namely an artificial neural network coupled to a genetic algorithm, in order to obtain more than sixty thousand flux configurations yielding to a scalar potential with at least one critical point. We observe that both stable AdS vacua with large moduli masses and small vacuum energy as well as unstable dS vacua with small tachyonic mass and large energy are absent, in accordance to the refined de Sitter conjecture. Moreover, by considering a hierarchy among fluxes, we observe that perturbative solutions with small values for the vacuum energy and moduli masses are favored, as well as scenarios in which the lightest modulus mass is much smaller than the corresponding AdS vacuum scale. Finally we apply some results on random matrix theory to conclude that the most probable mass spectrum derived from this string setup is that satisfying the Refined de Sitter and AdS scale conjectures.

Cosmological constant: Relaxation vs multiverse

We consider a scalar field with a bottom-less potential, such as g3ϕ, finding that cosmologies unavoidably end up with a crunch, late enough to be compatible with observations if g≲1.2H02/3MPl1/3. If rebounces avoid singularities, the multiverse acquires new features; in particular probabilities avoid some of the usual ambiguities. If rebounces change the vacuum energy by a small enough amount, this dynamics selects a small vacuum energy and becomes the most likely source of universes with anthropically small cosmological constant. Its probability distribution could avoid the gap by 2 orders of magnitude that seems left by standard anthropic selection.

Small vacuum energy from small equivalence violation in scalar gravity

The theory of scalar gravity proposed by Nordström, and refined by Einstein and Fokker, provides a striking analogy to general relativity. In its modern form, scalar gravity appears as the low-energy effective field theory of the spontaneous breaking of conformal symmetry within a CFT, and is AdS/CFT dual to the original Randall-Sundrum I model, but without a UV brane. Scalar gravity faithfully exhibits several qualitative features of the cosmological constant problem of standard gravity coupled to quantum matter, and the Weinberg no-go theorem can be extended to this case as well. Remarkably, a solution to the scalar gravity cosmological constant problem has been proposed, where the key is a very small violation of the scalar equivalence principle, which can be elegantly formulated as a particular type of deformation of the CFT. In the dual AdS picture this involves implementing Goldberger-Wise radion stabilization where the Goldberger-Wise field is a pseudo-Nambu Goldstone boson. In quantum gravity however, global symmetries protecting pNGBs are not expected to be fundamental. We provide a natural six-dimensional gauge theory origin for this global symmetry and show that the violation of the equivalence principle and the size of the vacuum energy seen by scalar gravity can naturally be exponentially small. Our solution may be of interest for study of non-supersymmetric CFTs in the spontaneously broken phase.

Varying vacuum energy of a self-interacting scalar field

Understanding mechanisms capable of altering the vacuum energy is currently of interest in field theories and cosmology. We consider an interacting scalar field and show that the vacuum energy naturally takes any value between its maximum and zero because interaction affects the number of operating field modes, the assertion that involves no assumptions or postulates. The mechanism is similar to the recently discussed temperature evolution of collective modes in liquids. The cosmological implication concerns the evolution of scalar field ϕ during the inflation of the Universe. ϕ starts with all field modes operating and maximal vacuum energy in the early inflation-dominated epoch. As a result of inflation, ϕ undergoes a dynamical crossover and arrives in the state with one long-wavelength longitudinal mode and small positive vacuum energy predicted to be asymptotically decreasing to zero in the late epoch. Accordingly, we predict that the currently observed cosmological constant will decrease in the future, and comment on the possibility of a cyclic Universe.

A Clifford-gravity-based cosmology, dark matter and dark energy

A Clifford-gravity-based model is exploited to build a generalized action (beyond the current ones used in the literature) and arrive at relevant numerical results which are consistent with the presently-observed de Sitter accelerating expansion of the universe driven by a very small vacuum energy density ρ obs ~ 10-120(MP)4 (MP is the Planck mass) and provide promising dark energy/matter candidates in terms of the 16 scalars corresponding to the degrees of freedom associated with a Cl (3, 1)-algebra-valued scalar field Φ in four dimensions.

Scale symmetry breaking from total derivative densities and the cosmological constant problem

The use in the action integral of totally divergent densities in generally coordinate invariant theories can lead to interesting mechanisms of spontaneous symmetry breaking of scale invariance. With dependence in the action on a metric independent density Φ, in 4D, we can define Φ=εμναβ∂μAναβ that gives a new interesting mechanism for breaking scale symmetry in 4D theories of gravity plus matter fields, through the Aναβ equations of motion which lead to an integration constant the breaks the scale symmetry, while introducing terms of the form eGlnK, e being the determinant of the vierbein, G being the Gauss–Bonnet scalar and K being scalar functions of the fields transforming like K→cK (where c is a constant) under a scale transformation. Such a term is invariant only up to a total divergence and therefore leads to breaking of scale invariance due to gravitational instantons. The topological density constructed out of gauge field strengths εμναβFμνaFαβa can be coupled to the dilaton field linearly to produce a scale invariant term up to a total divergence. The scale symmetry can be broken by Yang–Mills instantons which lead to a very small vacuum energy for our Universe.

The Cosmological Constant Puzzle: Vacuum Energies from QCD to Dark Energy

The accelerating expansion of the Universe points to a small positive vacuum energy density and negative vacuum pressure. A strong candidate is the cosmological constant in Einstein’s equations of General Relativity. The vacuum dark energy density extracted from astrophysics is 10 56 times smaller than the value expected from the Higgs potential in Standard Model particle physics. The dark energy scale is however close to the range of possible values expected for the light neutrino mass. We investigate this physics in a simple toy model where the chirality of the neutrino is treated by analogy as an Ising-like “spin” degree of freedom.

Inflation from flux cascades

When electric-type flux threads compact extra dimensions, a quantum nucleation event can break a flux line and initiate a cascade that unwinds many units of flux. Here, we present a novel mechanism for inflation based on this phenomenon. From the 4D point of view, the cascade begins with the formation of a bubble containing an open Friedmann–Robertson–Walker cosmology, but the vacuum energy inside the bubble is initially only slightly reduced, and subsequently decreases gradually throughout the cascade. If the initial flux number Q0≳O(100), during the cascade the universe can undergo N≳60 efolds of inflationary expansion with gradually decreasing Hubble constant, producing a nearly scale-invariant spectrum of adiabatic density perturbations with amplitude and tilt consistent with observation, and a potentially observable level of non-Gaussianity and tensor modes. The power spectrum has a small oscillatory component that does not decay away during inflation, with a period set approximately by the light-crossing time of the compact dimension(s). Since the ingredients are fluxes threading compact dimensions, this mechanism fits naturally into the string landscape, but does not appear to suffer from the eta problem or require fine-tuning (beyond the usual anthropic requirement of small vacuum energy after reheating).

A landscape in boundary string field theory: New class of solutions with massive state condensation

We solve the equation of motion of boundary string field theory allowing generic boundary operators quadratic in $X$, and explore string theory non-perturbative vacua with massive state condensation. Using numerical analysis, a large number of new solutions are found. Their energies turn out to distribute densely in the range between the D-brane tension and the energy of the tachyon vacuum. We discuss an interpretation of these solutions as perturbative closed string states. From the cosmological point of view, the distribution of the energies can be regarded as the so-called landscape of string theory, as we have a vast number of non-perturbative string theory solutions including one with small vacuum energy.

Extra-dimensional curvature suppression of the effective four-dimensional vacuum energy density

Considering a very large number of extra dimensions, N → ∞, we show that in the effective four-dimensional picture, to leading order in N, both the cosmological constant in N + 4 dimensions and the curvature of the extra dimensions (curved as spheres) give the same type of contributions. Furthermore, in this limit, the extra-dimensional curvature naturally suppresses the effect of a positive cosmological constant, so that the resulting effective potential governing the vacuum energy in the effective 4 − D picture has a leading 1/N dependence (i.e. vanishing in the large N limit). We can understand qualitatively this effect in a heuristic picture by thinking that both visible and extra dimensions have an equal sharing of the curvature caused by Λ. In this case when increasing the overall number of dimensions by adding N extra dimensions, then if N is large, the visible dimensions do not have to curve too much; hence, a small four-dimensional vacuum energy follows. In the large N picture, the potential can also be stabilized by a small (i.e. vanishing at large N) expectation value of a four-index field strength.

NONSINGULAR ORIGIN OF THE UNIVERSE AND THE COSMOLOGICAL CONSTANT PROBLEM

We consider a nonsingular origin for the universe starting from an Einstein static universe in the framework of a theory which uses two volume elements [Formula: see text] and Φd4x, where Φ is a metric independent density, also curvature, curvature square terms, first order formalism and for scale invariance a dilaton field ϕ are considered in the action. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for ϕ → ∞ relevant for the nonsingular origin of the universe and ϕ → -∞, describing our present universe. Surprisingly, avoidance of singularities and stability as ϕ → ∞ imply a positive but small vacuum energy as ϕ → -∞. Zero vacuum energy density for the present universe is the "threshold" for universe creation.

BIG BANG NUCLEOSYNTHESIS WITH A CONSTANT VACUUM ENERGY MOTIVATED BY CYCLIC COSMOLOGY

Abundances of primordial deuterium, [Formula: see text] and helium, Yp, are examined by modifying the early universe expansion rate and hence the time–temperature relation, including a constant vacuum energy motivated by the cyclic scenario of brane cosmology. Enhancement of abundances with respect to standard BBN prediction is found. Rapid expansion leads to early freeze-out of weak interaction and hence to an enhanced neutron fraction at elevated freeze-out temperature, which in turn results in more helium. Nucleosynthesis at a much lower temperature (due to rapid expansion) faces a larger Coulomb barrier and leaves more deuterium behind, which is also implied by a lower baryon-to-photon ratio (η) as we increase the vacuum energy density. The change in the helium fraction agrees within orders of magnitudes with that found by the effect of more neutrino flavors on Yp. Elevation of the neutron fraction at freeze-out is revealed by decrease in the neutron–proton mass difference (Q) from 1.293 MeV to 1.279 MeV, which is consistent with the study of the influence of extra dimension size on BBN. The lowest Q value corresponds to the highest vacuum energy and also to the largest size of the extra dimension. The upper limit on vacuum energy density is found by estimating the contribution from nonbaryonic dark matter by using X-ray emission from galaxy clusters and taking a flat spatial geometry, which is found to be the cosmological constant (Λ) observed today, so that the abundances do not run beyond the observational upper bounds. The allowed range of ΩΛ, 0.786 ≤ ΩΛ≤ 0.844, makes Ypand [Formula: see text] lie within the observational upper bounds, which yields a Big Bang equivalence of the Λ universe. This is expected to further motivate the cyclic scenario, which incorporates a small and constant vacuum energy density tied to spacetime.

Disordered locality as an explanation for the dark energy

We discuss a novel explanation of the dark energy as a manifestation of macroscopic nonlocality coming from quantum gravity, as proposed by Markopoulou [F. Markopoulou (private communication)]. It has been previously suggested that in a transition from an early quantum geometric phase of the Universe to a low temperature phase characterized by an emergent spacetime metric, locality might have been ``disordered.'' This means that there is a mismatch of micro-locality, as determined by the microscopic quantum dynamics and macro-locality as determined by the classical metric that governs the emergent low energy physics. In this paper we discuss the consequences for cosmology by studying a simple extension of the standard cosmological models with disordered locality. We show that the consequences can include a naturally small vacuum energy.

Vacuum energy of two-dimensionalN=(2,2)super Yang-Mills theory

We measure the vacuum energy of two-dimensional N=(2,2) super Yang-Mills theory using lattice simulation. The obtained vacuum energy density is E{sub 0}=0.09(9)((+10/-8))g{sup 2}, where the first error is the systematic and the second is the statistical one, measured in the dimensionful gauge coupling g which governs the scale of the system. The result is consistent with unbroken supersymmetry, although we cannot exclude a possible very small nonzero vacuum energy.

Limitations of anthropic predictions for the cosmological constant Λ: cosmic heat death of anthropic observers

This paper investigates anthropic bounds on the vacuum energy Λ by considering alternate starting assumptions. We first consider the possibility of cosmic observers existing at any random time (including the future) for constant Λ, and take into account the suppression of new structure formation as the universe approaches its eternal de Sitter (DS) geometry. Structures that collapse prior to the era of Λ-domination will lose causal contact with our Hubble volume within a finite (short) conformal time τ∗. Any remnants within our Hubble volume then suffer a cosmological heat death after the universe becomes DS. The probability for finding observers by random measurements in the volume bound by the de Sitter horizon is proportional to the rate of change in the ratio of the 3-volume V3(τ) to the 4-volume V4(τ), so that P ≃ 0. This vanishing probability of populated DS volumes is a simple consequence of the information loss problem for eternal DS spaces resulting from the finite and constant value of its temperature TDS ≃ Λ−1/2 and entropy S = 3/(GΛ). By contrast, for geometries with Λ = 0, structures can condense and entropy production can continue without bounds at any epoch. The probability of finding observers in Λ = 0 geometries is thus overwhelming higher than in DS spaces. As a result, anthropic reasoning does not explain the small but nonzero vacuum energy observed in our universe. We also address the case where observers are considered only at a specially chosen time—like the present epoch—but relax the allowed values of starting density fluctuations and hence the redshift of galaxy formation. In this latter case, the bounds on a Λ can be millions of times larger than previous estimates—and the observed value. We thus conclude that anthropic reasoning has limited predictive power.

Late Time Behavior of False Vacuum Decay: Possible Implications for Cosmology and Metastable Inflating States

We describe here how the late time behavior of the quantum mechanical decay of unstable states, which is predicted to deviate from an exponential form, may have important cosmological implications. It may increase the likelihood of eternal inflation and may enhance the likelihood of observing a small vacuum energy at late times versus possible late time decay into a large negative energy (anti-de Sitter space) vacuum state. Open questions include the following: How can internal observations made impact upon the wave function of the Universe and hence upon its decay characteristics?

ELECTROMAGNETIC DARK ENERGY

We introduce a new model for dark energy in the Universe in which a small cosmological constant is generated by ordinary electromagnetic vacuum energy. The corresponding virtual photons exist at all frequencies but switch from a gravitationally active phase at low frequencies to a gravitationally inactive phase at higher frequencies via a Ginzburg–Landau type of phase transition. Only virtual photons in the gravitationally active state contribute to the cosmological constant. A small vacuum energy density, consistent with astronomical observations, is naturally generated in this model. We propose possible laboratory tests for such a scenario based on phase synchronization in superconductors.

F-term uplifting via consistent D-terms

The issue of fine-tuning necessary to achieve satisfactory degree of hierarchy between moduli masses, the gravitino mass and the scale of the cosmological constant has been revisited in the context of supergravities with consistent D-terms. We have studied (extended) racetrack models where supersymmetry breaking and moduli stabilisation cannot be separated from each other. We show that even in such cases the realistic hierarchy can be achieved on the expense of a single fine-tuning. The presence of two condensates changes the role of the constant term in the superpotential, W_0, and solutions with small vacuum energy and large gravitino mass can be found even for very small values of W_0. Models where D-terms are allowed to vanish at finite vevs of moduli fields - denoted `cancellable' D-terms - and the ones where D-terms may vanish only at infinite vevs of some moduli - denoted `non-cancellable' - differ markedly in their properties. It turns out that the tuning with respect to the Planck scale required in the case of cancellable D-terms is much weaker than in the case of non-cancellable ones. We have shown that, against intuition, a vanishing D-term can trigger F-term uplifting of the vacuum energy due to the stringent constraint it imposes on vacuum expectation values of charged fields. Finally we note that our models only rely on two dimensionful parameters: M_P and W_0.

WHY THERE IS SOMETHING SO CLOSE TO NOTHING: TOWARDS A FUNDAMENTAL THEORY OF THE COSMOLOGICAL CONSTANT

The cosmological constant problem is turned around to argue for a new foundational physics postulate underlying a consistent quantum theory of gravity and matter, such as string theory. This postulate is a quantum equivalence principle which demands a consistent gauging of the geometric structure of canonical quantum theory. We argue that string theory can be formulated to accommodate such a principle, and that in such a theory the observed cosmological constant is a fluctuation about a zero value. This fluctuation arises from an uncertainty relation involving the cosmological constant and the effective volume of space–time. The measured, small vacuum energy is dynamically tied to the large "size" of the universe, thus violating naive decoupling between small and large scales. The numerical value is related to the scale of cosmological supersymmetry breaking, supersymmetry being needed for a nonperturbative stability of local Minkowski space–time regions in the classical regime.