Non-compact Space-time Dimensions Research Articles

Mini boson stars in higher dimensions are radially unstable

Boson stars are self-gravitating solutions made entirely of fundamental massive scalar fields. Here we investigate mini boson stars in D non-compact spacetime dimensions and we show that they are dynamically unstable for D>4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D>4$$\\end{document}.

Constraining the number of spacetime dimensions from GWTC-3 binary black hole mergers

In modified gravity models that allow for additional noncompact spacetime dimensions, energy from gravitational waves can leak into these extra spacetime dimensions, leading to a reduction in the amplitude of the observed gravitational waves, and thus are a source of potential systematics in the inferred luminosity distances to gravitational wave sources. Since binary black hole (BBH) mergers are standard sirens, we use the pair-instability supernova mass gap and its predicted features to determine a mass scale in order to break the mass-redshift degeneracy and thus infer the redshift of the source. We simultaneously fit the BBH population and the extra spacetime dimensions parameters from gravitational leakage models using BBH observations from the recently released GWTC-3 catalog. We set constraints on the number of spacetime dimensions and find that $D=3.9{3}_{\ensuremath{-}0.05}^{+0.08}$ at 68% C.L. for models that are independent of a screening scale, finding that the GWTC-3 constraint is as competitive as that set from GW170817 and its electromagnetic counterpart. For models where gravity leaks below a certain screening scale ${R}_{c}$, we find $D=4.4{9}_{\ensuremath{-}0.87}^{+1.63}$ and ${\mathrm{log}}_{10}\text{ }{R}_{c}/\mathrm{Mpc}=4.7{5}_{\ensuremath{-}0.99}^{+0.86}$ with a transition steepness ${\mathrm{log}}_{10}\text{ }n=0.8{5}_{\ensuremath{-}0.86}^{+0.76}$ for the leakage, which for the first time are constrained jointly with the BBH population at cosmological distances. These constraints are consistent with General Relativity (GR), where gravitational waves propagate in $D=3+1$ spacetime dimensions. Using the BBH population to probe modifications to standard cosmological models provides an independent test of GR that does not rely on any electromagnetic information but purely on gravitational wave observations.

Constraining extra dimensions on cosmological scales with LISA future gravitational wave siren data

The Universe is undergoing a late time acceleration. We investigate the idea that this acceleration could be the consequence of gravitational leakage into extra dimensions on cosmological scales rather than the result of a non-zero cosmological constant, and consider the ability of future gravitational-wave (GW) siren observations to probe this phenomenon and constrain the parameters of phenomenological models of this gravitational leakage. A gravitational space interferometer such as LISA will observe massive black hole binary (MBHB) merger events at cosmological distances, and will also provide sky localization information that may permit optical and other electromagnetic (EM) surveys to identify an EM counterpart of these events. In theories that include additional non-compact spacetime dimensions, the gravitational leakage intro extra dimensions leads to a reduction in the amplitude of observed gravitational waves and thereby a systematic discrepancy between the distance inferred to such sources from GW and EM observations. We investigate the capability of LISA to probe this modified gravity on large scales, specifically in the Dvali, Gabadadze and Porrati (DGP) model. Additionally, we include a Supernova Ia sample at lower redshift in order to explore the efficacy of this cosmological probe across a range of redshifts. We then use previously published simulated catalogues of cosmologically distant MBHB merger events detectable by LISA, and which are likely to produce an observable EM counterpart. We find that the extent to which LISA will be able to place limits on the number of spacetime dimensions and other cosmological parameters characterising modified gravity will strongly depend on the actual number and redshift distribution of sources, together with the uncertainty on the GW distance measurements. A relatively small number of sources (∼ 1) and high measurement uncertainties would strongly restrict the ability of LISA to place meaningful constraints on the parameters in cosmological scenarios where gravity is only five-dimensional and modified at scales larger than about ∼ 4 times the Hubble radius. Conversely, if the number of sources observed amounts to a four-year average of ∼ 27, then in the most favourable cosmological scenarios LISA has the potential to place meaningful constraints on the cosmological parameters—with a precision of ∼ 1% on the number of dimensions and ∼ 7.5% on the scale beyond which gravity is modified, thereby probing the late expansion of the universe up to a redshift of ∼ 8, i.e. on scales not yet tested by present EM observations.

Limits on the number of spacetime dimensions from GW170817

The observation of GW170817 in both gravitational and electromagnetic waves provides a number of unique tests of general relativity. One question we can answer with this event is: do large-wavelength gravitational waves and short-frequency photons experience the same number of spacetime dimensions? In models that include additional non-compact spacetime dimensions, as the gravitational waves propagate, they “leak” into the extra dimensions, leading to a reduction in the amplitude of the observed gravitational waves, and a commensurate systematic error in the inferred distance to the gravitational wave source. Electromagnetic waves would remain unaffected. We compare the inferred distance to GW170817 from the observation of gravitational waves, dLGW, with the inferred distance to the electromagnetic counterpart NGC 4993, dLEM. We constrain dLGW = (dLEM/Mpc)γ with γ = 1.01+0.04−0.05 (for the SHoES value of H0) or γ = 0.99+0.03−0.05 (for the Planck value of H0), where all values are MAP and minimal 68% credible intervals. These constraints imply that gravitational waves propagate in D=3+1 spacetime dimensions, as expected in general relativity. In particular, we find that D = 4.02+0.07−0.10 (SHoES) and D = 3.98+0.07−0.09 (Planck). Furthermore, we place limits on the screening scale for theories with D>4 spacetime dimensions, finding that the screening scale must be greater than ∼ 20 Mpc. We also place a lower limit on the lifetime of the graviton of t > 4.50 × 108 yr.

Subleading soft theorem for multiple soft gravitons

We derive the subleading soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. Our results are valid to all orders in perturbation theory when the number of non-compact space-time dimensions is six or more, but only for tree amplitudes for five or less non-compact space-time dimensions due to enhanced contribution to loop amplitudes from the infrared region.

Subleading soft graviton theorem for loop amplitudes

Superstring field theory gives expressions for heterotic and type II string loop amplitudes that are free from ultraviolet and infrared divergences when the number of non-compact space-time dimensions is five or more. We prove the subleading soft graviton theorem in these theories to all orders in perturbation theory for S-matrix elements of arbitrary number of finite energy external states but only one external soft graviton. We also prove the leading soft graviton theorem for arbitrary number of finite energy external states and arbitrary number of soft gravitons. Since our analysis is based on general properties of one particle irreducible effective action, the results are valid in any theory of quantum gravity that gives finite result for the S-matrix order by order in perturbation theory without violating general coordinate invariance.

Macroscopic fundamental strings in cosmology

We show that, when D⪖4, theories of closed strings of closed strings in D, non-compact space-time dimensions exhibit a phase transition. The high-temperature phase is characterized by a condensate of arbitrarily long strings with Hausdorff dimension two (area filling curves). We suggest that this stringy phase is the ancestor of the adiabatic era. Fundamental strings could then both drive the inflation and seed, in a way reminiscent of the cosmic string mechanism, the large structures in the universe.