Introduction to causal sets and their phenomenology

In this introduction to the causal set approach to the problem of quantum gravity, I emphasise that causal sets are both fundamentally discrete and Lorentz invariant, which makes them nonlocal. I focus on opportunities for phenomenology arising from and stimulated by causal sets.

[1]  N. Kaloper,et al.  Low energy bounds on Poincaré violation in causal set theory , 2006, astro-ph/0607485.

[2]  B. Rothschild,et al.  Asymptotic enumeration of partial orders on a finite set , 1975 .

[3]  Rafael D. Sorkin,et al.  DISCRETENESS WITHOUT SYMMETRY BREAKING: A THEOREM , 2006, gr-qc/0605006.

[4]  R. Sorkin.  Stochastic evolution on a manifold of states , 1986 .

[5]  Maqbool Ahmed,et al.  Everpresent Λ. II. Structural stability , 2012, 1210.2589.

[6]  R. Sorkin,et al.  Evidence for a continuum limit in causal set dynamics , 2000, gr-qc/0003117.

[7]  Seth Major,et al.  Stable homology as an indicator of manifoldlikeness in causal set theory , 2009, 0902.0434.

[8]  David Rideout,et al.  Indications of de Sitter Spacetime from Classical Sequential Growth Dynamics of Causal Sets , 2009, 0909.4771.

[9]  Might Quantum-Induced Deviations from the Einstein Equations Detectably Affect Gravitational Wave Propagation? , 2013, 1304.4981.

[10]  R. Sorkin,et al.  “Renormalization” transformations induced by cycles of expansion and contraction in causal set cosmology , 2000, gr-qc/0009063.

[11]  B. Riemann.  Über die Hypothesen, welche der Geometrie zu Grunde liegen , 1868 .

[12]  Onkar Parrikar,et al.  Causal topology in future and past distinguishing spacetimes , 2011, 1102.0936.

[13]  R. Sorkin,et al.  Energy-momentum diffusion from spacetime discreteness , 2008, 0810.5591.

[14]  Joe Henson,et al.  QUANTUM GRAVITY PHENOMENOLOGY, LORENTZ INVARIANCE AND DISCRETENESS , 2003, gr-qc/0311055.

[15]  S. Hawking,et al.  Cosmological Event Horizons, Thermodynamics, and Particle Creation , 1977 .

[16]  Moore.  Comment on "Space-time as a causal set" , 1988, Physical review letters.

[17]  Bombelli,et al.  Space-time as a causal set. , 1987, Physical review letters.

[18]  George F. R. Ellis,et al.  The Large Scale Structure of Space-Time , 2023 .

[19]  Rafael D. Sorkin.  Forks in the road, on the way to quantum gravity , 1997 .

[20]  Gregory,et al.  Structure of random discrete spacetime. , 1990, Physical review letters.

[21]  R. Sorkin.  Quantum mechanics as quantum measure theory , 1994, gr-qc/9401003.

[22]  Sorkin.  Toward a proof of entropy increase in the presence of quantum black holes. , 1986, Physical review letters.

[23]  R. Sorkin.  Approaches to Quantum Gravity: Does locality fail at intermediate length scales? , 2007, gr-qc/0703099.

[24]  A Lorentzian Gromov–Hausdorff notion of distance , 2003, gr-qc/0308074.

[25]  Fay Dowker,et al.  Causal set d'Alembertians for various dimensions , 2013, 1305.2588.

[26]  Maqbool Ahmed,et al.  Everpresent Lambda , 2002, astro-ph/0209274.

[27]  J. Schwarz.  Elementary Particles and the Universe , 1991 .

[28]  D. Malament.  The class of continuous timelike curves determines the topology of spacetime , 1977 .

[29]  Rafael D. Sorkin.  Indications of Causal Set Cosmology , 1998 .

[30]  Carlo Rovelli.  Quantum gravity , 2008, Scholarpedia.

[31]  Seth Major,et al.  On Recovering continuum topology from a causal set , 2007 .

[32]  Bombelli,et al.  Bombelli et al. reply. , 1988, Physical review letters.

[33]  Sumati Surya.  Evidence for the continuum in 2D causal set quantum gravity , 2011 .

[34]  Andrew King,et al.  A new topology for curved space–time which incorporates the causal, differential, and conformal structures , 1976 .

[35]  R. Sorkin,et al.  Classical sequential growth dynamics for causal sets , 1999, gr-qc/9904062.

[36]  R. Dudley.  Lorentz-invariant Markov processes in relativistic phase space , 1966 .

[37]  S. Johnston.  Feynman propagator for a free scalar field on a causal set. , 2009, Physical review letters.

[38]  Soviet Union. Vysshiĭ sovet narodnogo khozi︠a︡ĭstva,et al.  Physikalische Zeitschrift der Sowjetunion , 1932 .

[39]  M. Lévy,et al.  Recent developments in gravitation , 1979 .

[40]  Fay Dowker,et al.  Scalar curvature of a causal set. , 2010, Physical review letters.

[41]  J. Henson,et al.  Approaches to Quantum Gravity: The causal set approach to Quantum Gravity , 2006, gr-qc/0601121.

[42]  Hawking,et al.  Chronology protection conjecture. , 1992, Physical review. D, Particles and fields.

[43]  D. Meyer.  The dimension of causal sets , 1988 .

[44]  R. Penrose.  Techniques of Differential Topology in Relativity , 1972 .

[45]  Statistical Lorentzian geometry and the closeness of Lorentzian manifolds , 2000, gr-qc/0002053.