IT HAS BEEN RECENTLY POINTED OUT BY MITHANI-VILENKIN [1-4] THAT CERTAIN EMERGENT UNIVERSE SCENARIOS WHICH ARE CLASSICALLY STABLE ARE NEVERTHELESS UNSTABLE SEMICLASSICALLY TO COLLAPSE. HERE, WE SHOW THAT THERE IS A CLASS OF EMERGENT UNIVERSES DERIVED FROM SCALE INVARIANT TWO MEASURES THEORIES WITH SPONTANEOUS SYMMETRY BREAKING (S.S.B) OF THE SCALE INVARIANCE, WHICH CAN HAVE BOTH CLASSICAL STABILITY AND DO NOT SUFFER THE INSTABILITY POINTED OUT BY MITHANI-VILENKIN TOWARDS COLLAPSE. WE FIND THAT THIS STABILITY IS DUE TO THE PRESENCE OF A SYMMETRY IN THE ?EMERGENT PHASE?, WHICH TOGETHER WITH THE NON LINEARITIES OF THE THEORY, DOES NOT ALLOW THAT THE FLRW SCALE FACTOR TO BE SMALLER THAT A CERTAIN MINIMUM VALUE A0 IN A CERTAIN PROTECTED REGION.

WE CONSIDER A NON-SINGULAR ORIGIN FOR THE UNIVERSE STARTING FROM AN EINSTEIN STATIC UNIVERSE, THE SO CALLED EMERGENT UNIVERSE SCENARIO, IN THE FRAMEWORK OF A THEORY WHICH USES TWO VOLUME ELEMENTS $\SQRT{-{G}}D^{4}X$ AND $\PHI D^{4}X$, WHERE $\PHI $ IS A METRIC INDEPENDENT DENSITY, USED AS AN ADDITIONAL MEASURE OF INTEGRATION. ALSO CURVATURE, CURVATURE SQUARE TERMS AND FOR SCALE INVARIANCE A DILATON FIELD $\PHI$ ARE CONSIDERED IN THE ACTION. THE FIRST ORDER FORMALISM IS APPLIED. THE INTEGRATION OF THE EQUATIONS OF MOTION ASSOCIATED WITH THE NEW MEASURE GIVES RISE TO THE SPONTANEOUS SYMMETRY BREAKING (S.S.B) OF SCALE INVARIANCE (S.I.). AFTER S.S.B. OF S.I., IT IS FOUND THAT A NON TRIVIAL POTENTIAL FOR THE DILATON IS GENERATED. 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 $\PHI \RIGHTARROW \INFTY$ RELEVANT FOR THE NON SINGULAR ORIGIN OF THE UNIVERSE, FOLLOWED BY AN INFLATIONARY PHASE AND $\PHI \RIGHTARROW -\INFTY$, DESCRIBING OUR PRESENT UNIVERSE. THE DYNAMICS OF THE SCALAR FIELD BECOMES NON LINEAR AND THESE NON LINEARITIES PRODUCE A NON TRIVIAL VACUUM STRUCTURE FOR THE THEORY AND ARE RESPONSIBLE FOR THE STABILITY OF SOME OF THE EMERGENT UNIVERSE SOLUTIONS, WHICH EXISTS FOR A PARAMETER RANGE OF VALUES OF THE VACUUM ENERGY IN $\PHI \RIGHTARROW -\INFTY$, WHICH MUST BE POSITIVE BUT NOT VERY BIG, AVOIDING THE EXTREME FINE TUNING REQUIRED TO KEEP THE VACUUM ENERGY DENSITY OF THE PRESENT UNIVERSE SMALL. THE NON TRIVIAL VACUUM STRUCTURE IS CRUCIAL TO ENSURE THE SMOOTH TRANSITION FROM THE EMERGING PHASE, TO AN INFLATIONARY PHASE AND FINALLY TO THE SLOWLY ACCELERATED UNIVERSE NOW. ZERO VACUUM ENERGY DENSITY FOR THE PRESENT UNIVERSE DEFINES THE THRESHOLD FOR THE CREATION OF THE UNIVERSE.

IN THIS PAPER WE STUDY FINITE TIME FUTURE SINGULARITIES IN ANISOTROPIC BIANCHI TYPE I MODELS. IT IS SHOWN THAT THERE EXIST FUTURE SINGULARITIES SIMILAR TO BIG RIP ONES (WHICH APPEAR IN THE FRAMEWORK OF PHANTOM FRIEDMANN-ROBERTSON-WALKER COSMOLOGIES). SPECIFICALLY, IN AN ELLIPSOIDAL ANISOTROPIC SCENARIO OR IN A FULLY ANISOTROPIC SCENARIO, THE THREE DIRECTIONAL AND AVERAGE SCALE FACTORS MAY DIVERGE AT A FINITE FUTURE TIME, TOGETHER WITH ENERGY DENSITIES AND ANISOTROPIC PRESSURES. WE CALL THESE SINGULARITIES ?ANISOTROPIC BIG RIP SINGULARITIES.? WE SHOW THAT THERE ALSO EXIST BIANCHI TYPE I MODELS FILLED WITH MATTER, WHERE ONE OR TWO DIRECTIONAL SCALE FACTORS MAY DIVERGE. ANOTHER TYPE OF FUTURE ANISOTROPIC SINGULARITIES IS SHOWN TO BE PRESENT IN VACUUM COSMOLOGIES, I.E., KASNER SPACETIMES. THESE SINGULARITIES ARE INDUCED BY THE SHEAR SCALAR, WHICH ALSO BLOWS UP AT A FINITE TIME. WE CALL SUCH A SINGULARITY ?VACUUM RIP.? IN THIS CASE ONE DIRECTIONAL SCALE FACTOR BLOWS UP, WHILE THE OTHER TWO AND AVERAGE SCALE FACTORS TEND TO ZERO.

A NEW CLASS OF GRAVITY-MATTER MODELS DEFINED IN TERMS OF TWO INDEPENDENT NON-RIEMANNIAN VOLUME FORMS (ALTERNATIVE GENERALLY COVARIANT INTEGRATION MEASURE DENSITIES) ON THE SPACE-TIME MANIFOLD ARE STUDIED IN SOME DETAIL. THESE MODELS INVOLVE AN ADDITIONAL R2 (SQUARE OF THE SCALAR CURVATURE) TERM AS WELL AS SCALAR MATTER FIELD POTENTIALS OF APPROPRIATE FORM SO THAT THE PERTINENT ACTION IS INVARIANT UNDER GLOBAL WEYL-SCALE SYMMETRY. SCALE INVARIANCE IS SPONTANEOUSLY BROKEN UPON INTEGRATION OF THE EQUATIONS OF MOTION FOR THE AUXILIARY VOLUME-FORM DEGREES OF FREEDOM. AFTER PERFORMING TRANSITION TO THE PHYSICAL EINSTEIN FRAME WE OBTAIN: (I) AN EFFECTIVE POTENTIAL FOR THE SCALAR FIELD WITH TWO FLAT REGIONS WHICH ALLOWS FOR A UNIFIED DESCRIPTION OF BOTH EARLY UNIVERSE INFLATION AS WELL AS OF PRESENT DARK ENERGY EPOCH; (II) FOR A DEFINITE PARAMETER RANGE THE MODEL POSSESSES A NON-SINGULAR """"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""EMERGENT UNIVERSE"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" SOLUTION WHICH DESCRIBES AN INITIAL PHASE OF EVOLUTION THAT PRECEDES THE INFLATIONARY PHASE; (III) FOR A REASONABLE CHOICE OF THE PARAMETERS THE PRESENT MODEL CONFORMS TO THE PLANCK COLLABORATION DATA.

IN THIS WORK WE PROPOSE AN ALTERNATIVE SCHEME FOR AN EMERGENT UNIVERSE SCENARIO WHERE THE UNIVERSE IS INITIALLY IN A STATIC STATE SUPPORTED BY A SCALAR FIELD LOCATED IN A FALSE VACUUM. THE UNIVERSE BEGINS TO EVOLVE WHEN, BY QUANTUM TUNNELING, THE SCALAR FIELD DECAYS INTO A STATE OF TRUE VACUUM. THE EMERGENT UNIVERSE MODELS ARE INTERESTING SINCE THEY PROVIDE SPECIFIC EXAMPLES OF NONSINGULAR INFLATIONARY UNIVERSES.

IN THIS WORK WE STUDY AN ALTERNATIVE SCHEME FOR AN EMERGENT UNIVERSE SCENARIO IN THE CONTEXT OF A JORDAN-BRANS-DICKE THEORY, WHERE THE UNIVERSE IS INITIALLY IN A TRULY STATIC STATE SUPPORTED BY A SCALAR FIELD LOCATED IN A FALSE VACUUM. THE MODEL PRESENTS A CLASSICALLY STABLE PAST ETERNAL STATIC STATE WHICH IS BROKEN WHEN, BY QUANTUM TUNNELING, THE SCALAR FIELD DECAYS INTO A STATE OF TRUE VACUUM AND THE UNIVERSE BEGINS TO EVOLVE FOLLOWING THE EXTENDED OPEN INFLATIONARY SCHEME.

THE DILATON-GRAVITY SECTOR OF A LINEAR IN THE SCALAR CURVATURE, SCALE INVARIANT TWO MEASURES FIELD THEORY (TMT), IS EXPLORED IN DETAIL IN THE CONTEXT OF CLOSED FRW COSMOLOGY AND SHOWN TO ALLOW STABLE EMERGING UNIVERSE SOLUTIONS. THE MODEL POSSESSES SCALE INVARIANCE WHICH IS SPONTANEOUSLY BROKEN DUE TO THE INTRINSIC FEATURES OF THE TMT DYNAMICS. WE STUDY THE TRANSITION FROM THE EMERGING PHASE TO INFLATION, AND THEN TO A ZERO COSMOLOGICAL CONSTANT PHASE. WE ALSO STUDY THE SPECTRUM OF DENSITY PERTURBATIONS AND THE CONSTRAINTS THAT IMPOSE ON THE PARAMETERS OF THE THEORY.

IN THIS PAPER, BASED ON PHYS. REV. D 91, NO. 8, 083534 (2015), WE STUDY SUPER INFLATION IN THE CONTEXT OF THE EMERGENT UNIVERSE (EU) SCENARIO. THE EXISTENCE OF A SUPER INFLATING PHASE BEFORE THE ONSET OF SLOW ROLL INFLATION ARISES IN ANY EMERGENT UNIVERSE MODEL. WE FOUND THAT THE SUPER INFLATIONARY PERIOD IN THE EU SCENARIO PRODUCES A SUPPRESSION OF THE CMB ANISOTROPIES AT LARGE SCALE WHICH COULD BE RESPONSIBLE OF THE OBSERVED LACK OF POWER AT LARGE ANGULAR SCALES OF THE CMB.

WE CONSIDER A SCALE INVARIANT MODEL WHICH INCLUDES A $R^{2}$ TERM IN ACTION AND SHOW THAT A STABLE "EMERGING UNIVERSE" SCENARIO IS POSSIBLE. THE MODEL BELONGS TO THE GENERAL CLASS OF THEORIES, WHERE AN INTEGRATION MEASURE INDEPENDENT OF THE METRIC IS INTRODUCED. TO IMPLEMENT SCALE INVARIANCE (S.I.), A DILATON FIELD IS INTRODUCED. THE INTEGRATION OF THE EQUATIONS OF MOTION ASSOCIATED WITH THE NEW MEASURE GIVES RISE TO THE SPONTANEOUS SYMMETRY BREAKING (S.S.B) OF S.I. AFTER S.S.B. OF S.I. IN THE MODEL WITH THE $R^{2}$ TERM (AND FIRST ORDER FORMALISM APPLIED), IT IS FOUND THAT A NON TRIVIAL POTENTIAL FOR THE DILATON IS GENERATED. THE DYNAMICS OF THE SCALAR FIELD BECOMES NON LINEAR AND THESE NON LINEARITIES ARE INSTRUMENTAL IN THE STABILITY OF SOME OF THE EMERGING UNIVERSE SOLUTIONS, WHICH EXISTS FOR A PARAMETER RANGE OF THE THEORY.

THE INSTANT PREHEATING MECHANISM IN THE FRAMEWORK OF A SCALE INVARIANT TWO MEASURES THEORY IS STUDIED. WE INTRODUCE THIS MECHANISM INTO A NONOSCILLATING INFLATIONARY MODEL AS ANOTHER POSSIBLE SOLUTION TO THE REHEATING OF THE UNIVERSE IN THIS THEORY. IN THIS FRAMEWORK, WE CONSIDER THAT THE MODEL INCLUDES TWO SCALAR MATTER FIELDS, THE FIRST IS A DILATON FIELD THAT TRANSFORMS UNDER SCALE TRANSFORMATIONS AND WILL BE CONSIDERED ALSO AS THE FIELD THAT DRIVES INFLATION, AND THE SECOND IS A SCALAR FIELD THAT WILL INTERACT WITH THE INFLATON THROUGH AN EFFECTIVE POTENTIAL. BY ASSUMING THIS INTERACTION TERM, WE OBTAIN A SCENARIO OF INSTANT RADIATION OR DECAY OF PARTICLES ACCORDING TO THE DOMAIN THE EFFECTIVE MASS OF THE FIELD THAT INTERACTS WITH THE INFLATON. ALSO, WE CONSIDER A SCALE INVARIANT YUKAWA INTERACTION. AFTER PERFORMING THE TRANSITION TO THE PHYSICAL EINSTEIN FRAME, WE OBTAIN AN EXPRESSION FOR THE DECAY RATE FROM OUR SCALAR FIELD GOING INTO TWO FERMIONS. BESIDES, FROM SPECIFIC DECAY RATES, DIFFERENT CONSTRAINTS AND BOUNDS FOR THE COUPLING PARAMETERS ASSOCIATED WITH OUR MODEL ARE FOUND.

IN THIS PAPER, BASED ON JCAP 1608 (2016) 049, WE SHOW THAT THERE IS A CLASS OF EMERGENT UNIVERSES MODELS, DERIVED FROM SCALE INVARIANT TWO MEASURES THEORIES WITH SPONTANEOUS SYMMETRY BREAKING (S.S.B) OF THE SCALE INVARIANCE, WHICH CAN HAVE BOTH CLASSICAL STABILITY AND DO NOT SUFFER THE INSTABILITY POINTED OUT BY MITHANI-VILENKIN TOWARDS COLLAPSE [4, 3, 2, 5]. WE FIND THAT THIS STABILITY IS DUE TO THE PRESENCE OF A SYMMETRY IN THE """"""""EMERGENT PHASE"""""""", WHICH TOGETHER WITH THE NON LINEARITIES OF THE THEORY, DOES NOT ALLOW THAT THE FLRW SCALE FACTOR TO BE SMALLER THAT A CERTAIN MINIMUM VALUE A 0 IN A CERTAIN PROTECTED REGION.

BASED ON AN EARLIER INTRODUCED NEW CLASS OF GENERALIZED GRAVITY-MATTER MODELS DEFINED IN TERMS OF TWO INDEPENDENT NONRIEMANNIAN VOLUME FORMS (ALTERNATIVE GENERALLY COVARIANT INTEGRATION MEASURE DENSITIES) ON THE SPACE-TIME MANIFOLD, WE DERIVE AN EFFECTIVE ?EINSTEIN-FRAME? THEORY FEATURING THE FOLLOWING REMARKABLE PROPERTIES: (I) WE OBTAIN EFFECTIVE POTENTIAL FOR THE COSMOLOGICAL SCALAR FIELD POSSESSING TWO INFINITELY LARGE FLAT REGIONS WHICH ALLOWS FOR A UNIFIED DESCRIPTION OF BOTH EARLY UNIVERSE INFLATION AS WELL AS OF PRESENT DARK ENERGY EPOCH; (II) FOR A SPECIFIC PARAMETER RANGE THE MODEL POSSESSES A NON-SINGULAR STABLE ?EMERGENT UNIVERSE? SOLUTION WHICH DESCRIBES AN INITIAL PHASE OF EVOLUTION THAT PRECEDES THE INFLATIONARY PHASE.

WE PRESENT AN ALTERNATIVE SCHEME FOR AN EMERGENT UNIVERSE SCENARIO, DEVELOPED PREVIOUSLY IN $PHYS.\ REV.\ D {\BF 86}, 083524 (2012)$, WHERE THE UNIVERSE IS INITIALLY IN A STATIC STATE SUPPORTED BY A SCALAR FIELD LOCATED IN A FALSE VACUUM. THE UNIVERSE BEGINS TO EVOLVE WHEN, BY QUANTUM TUNNELING, THE SCALAR FIELD DECAYS INTO A STATE OF TRUE VACUUM. THE EMERGENT UNIVERSE MODELS ARE INTERESTING SINCE THEY PROVIDE SPECIFIC EXAMPLES OF NON-SINGULAR INFLATIONARY UNIVERSES.

IN THIS WORK IT IS PROPOSED AN ALTERNATIVE SCHEME FOR AN EMERGENT UNIVERSE SCENARIO IN THE CONTEXT OF A JORDAN-BRANS-DICKE THEORY, WHERE THE UNIVERSE IS INITIALLY IN A STATIC STATE SUPPORTED BY A SCALAR FIELD LOCATED IN A FALSE VACUUM. THE UNIVERSE BEGINS TO EVOLVE WHEN, BY QUANTUM TUNNELING, THE SCALAR FIELD DECAYS INTO A STATE OF TRUE VACUUM. IN PARTICULAR, IN THIS WORK WE STUDY THE STABILITY OF THE STATIC UNIVERSE, UNDER THE AFOREMENTIONED CHARACTERISTICS, AND THE PROBABILITY OF CREATING A TRUE VACUUM BUBBLE. IT IS SHOWN THAT IN THIS MODEL, UNLIKE WHAT HAPPENS IN PREVIOUS WORKS, THE STATIC UNIVERSE IS STABLE UNDER SMALL CLASSICAL PERTURBATIONS.