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P. J. E. Peebles and Bharat Ratra- The cosmological constant and dark energy

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The cosmological constant and dark energy P. J. E. Peebles Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544 Bharat Ratra Department of Physics, Kansas State University, Manhattan, Kansas 66506 (Publi shed 22 April 20 03) Physics welcomes the idea that space contains energy whose gravitational effect approximates that of Einstein’s cosmological constant, ; today the concept is termed dark energy or quintessence. Physics also suggests that dark energy could be dynamical, allowing for the arguably appealing picture of an evo lvi ng dar k-e ner gy den sit y app roa chi ng its nat ura l val ue, zer o, and sma ll now bec ause the expanding universe is old. This would alleviate the classical problem of the curious energy scale of a milli elect ron volt associated with a constant . Dark energy may have been detected by recent cosmol ogi cal tes ts. The se tests mak e a goo d scientific case for the conte xt, in the rel ati vis tic Friedmann-Lemaı  ˆ tre model, in which the gravitational inverse-square law is applied to the scales of cosmo logy . We have well-ch ecked eviden ce that the mean mass density is not much more than one-quarter of the critical Einstein– de Sitter value. The case for detection of dark energy is not yet as convincing but still serious; we await more data, which may be derived from work in progress. Planned observations may detect the evolution of the dark-ene rgy density; a posit ive result would be a considerable stimulus for attempts at understanding the microphysics of dark energy. This review presents the basic physics and astronomy of the subject, reviews the history of ideas, assesses the state of the observational evidence, and comments on recent developments in the search for a fundamental theory. CONTENTS I. Introduction 559 A. The issues for observational cosmology 560 B. The opportunity for physics 561 C. Some explanations 562 II. Basic Concepts 563 A. The Friedmann-Le maı  ˆ tre model 563 B. The cosmological constant 565 C. Inflation and dark energy 566 III. Historical Remarks 567 A. Einstein’ s thoughts 567 B. The development of ideas 569 1. Earl y i ndica tions of  569 2. The co incid ences a rgument ag ains t 570 3. V acuum ener gy and 570 C. Inflation 572 1. The scenario 572 2. Inflation in a low-density universe 573 D. The cold-dark-matter model 574 E. Dark energy 576 1. The XCDM parametrization 576 2. De ca y by e mi ss i on of m at te r or r ad ia ti o n 5 77 3. Cosmic field defects 578 4. Dark-energy scalar field 578 IV . The Cosmological Tests 580 A. The theories 580 1. General relativity 580 2. The col d-da rk-matte r model fo r structure formation 582 B. The tests 584 1. Ther mal cos mic mi crowa ve back groun d radiation 585 2. Light-element abundances 585 3. Expansion times 586 4. The redshift-angular-size and redshift- magnitude relations 587 5. Galaxy counts 588 6. The gravitational lensing rate 588 7. Dynamics and the mean mass density 589 8. The baryon mass fractio n in clus ters of galaxies 590 9. The cluster mass function 590 10. Biasing and the development of nonlinear mass density fluctuations 590 11. The anisotropy of the cosmic microwave background radiation 591 12. The mass autocorrelati on function and nonbaryonic matter 593 13. The gra vi ta ti on al inv er se -s qu ar e law 59 3 C. The state of the cosmological tests 594 V . Concluding Remarks 595 Note added in proof 596 Acknowledgments 597 Appe ndix : Re cent Da rk-Ene rg y Scal ar Fi el d Re sear ch 59 7 References 599 I. INTRODUCTION There is significant observational evidence for the de- tection of Einstein’s cosmological constant, , or a com- ponent of the material content of the universe that var- ies only slowly with time and space and so acts like . We shall use the term dark energy for or a compon ent that acts like it. Detection of dark energy would be a new clue to an old puzzle: the gravitational effect of the zero-point energies of particles and fields. The total with ot her ener gie s, that are cl os e to homoge neous and nearly independent of time, acts as dark energy. What is REVIEWS OF MODERN PHYSICS, VOLUME 75, APRIL 2003 0034-6861/2003/75(2)/559(48)/$35.00 ©2003 The American Physical Society 559
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