Curvature dark energy reconstruction through different cosmographic distance definitions. Issue 7 (25th July 2014)

• Record Type: Journal Article
• Authors: Capozziello, Salvatore; De Laurentis, Mariafelicia; Luongo, Orlando; Battye, Richard; Goobar, Ariel; Weller, Jochen
• Is Part Of: Annalen der Physik. Volume 526:Issue 7/8(2014:Jul.)
• Page Start: 309
• Page End: 317
• Publication Date: 2014-07-25
• Subjects: Physics -- Periodicals; Chemistry -- Periodicals; 530.05
• DOI: 10.1002/andp.201400049
• Languages: English
• ISSNs: 0003-3804

Abstract

<abstract abstract-type="short" xml:lang="en" id="andp201400049-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p>In the context of <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh112zzck0" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00033804:andp201400049:equation:andp201400049-math-0018" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="script">R</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> gravity, dark energy is a geometrical fluid with negative equation of state. Since the function <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh112zzcn3" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00033804:andp201400049:equation:andp201400049-math-0019" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="script">R</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> is not known <italic>a priori</italic>, the need of a model independent reconstruction of its shape represents a relevant technique to determine which <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh112zzdgv" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00033804:andp201400049:equation:andp201400049-math-0020" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="script">R</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> model is really favored with respect to others. To this aim, cosmography is related to a generic <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh112zzdjz" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00033804:andp201400049:equation:andp201400049-math-0021" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="script">R</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> and its derivatives in order to provide a model‐independent investigation at redshift <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh112zzdm2" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00033804:andp201400049:equation:andp201400049-math-0022" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>z</mml:mi><mml:mo>∼</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>. The analysis is based on the use of three different cosmological distance definitions, in order to alleviate the duality problem, i.e. the problem of which cosmological distance to use with specific cosmic data sets. Therefore, the luminosity, <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh112zzdnm" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00033804:andp201400049:equation:andp201400049-math-0023" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>d</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:math></alternatives></inline-formula>, flux, <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh112zzdbn" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00033804:andp201400049:equation:andp201400049-math-0024" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>d</mml:mi><mml:mi>F</mml:mi></mml:msub></mml:math></alternatives></inline-formula>, and angular, <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh112zzdc6" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00033804:andp201400049:equation:andp201400049-math-0025" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>d</mml:mi><mml:mi>A</mml:mi></mml:msub></mml:math></alternatives></inline-formula>, distances are considered and numerical constraints by the Union 2.1 supernovae compilation and measurement of baryonic acoustic oscillations, at <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh112zzddr" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00033804:andp201400049:equation:andp201400049-math-0026" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>z</mml:mi><mml:mrow><mml:mi>B</mml:mi><mml:mi>A</mml:mi><mml:mi>O</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0.35</mml:mn></mml:mrow></mml:math></alternatives></inline-formula> are found. It was noticed that all distances reduce to the same expression, i.e. <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh112zzdf9" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00033804:andp201400049:equation:andp201400049-math-0027" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>L</mml:mi><mml:mo>;</mml:mo><mml:mi>F</mml:mi><mml:mo>;</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:msub><mml:mo>∼</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:msub><mml:mi mathvariant="script">H</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mfrac><mml:mi>z</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>, at first order. Thus, to fix the cosmographic series of observables, the initial value of <italic>H</italic><sub>0</sub> was imposed by fitting <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh112zzbwf" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00033804:andp201400049:equation:andp201400049-math-0028" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="script">H</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math></alternatives></inline-formula> through supernovae only, in the redshift regime <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh112zzbvw" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00033804:andp201400049:equation:andp201400049-math-0029" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>z</mml:mi><mml:mo><</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>. The pressure of curvature dark energy fluid was found to be slightly lower than the one related to the cosmological constant. This indicates that a possible evolving curvature dark energy realistically fills the current universe. Moreover, the combined use of <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh112zzc81" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00033804:andp201400049:equation:andp201400049-math-0030" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo>, </mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mi>F</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula> and <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh112zzccp" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00033804:andp201400049:equation:andp201400049-math-0031" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>d</mml:mi><mml:mi>A</mml:mi></mml:msub></mml:math></alternatives></inline-formula> shows that the sign of the acceleration parameter agrees with theoretical bounds, while its variation, namely the jerk parameter, is compatible with <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh112zzcd7" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00033804:andp201400049:equation:andp201400049-math-0032" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>j</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>></mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>. Finally, the functional form of <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh112zzc9k" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00033804:andp201400049:equation:andp201400049-math-0033" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="script">R</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula> is infered by means of a truncated polynomial approximation, in terms of fourth order scale factor <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh112zzcb4" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00033804:andp201400049:equation:andp201400049-math-0034" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>a</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></alternatives></inline-formula>. <boxed-text content-type="graphic" position="anchor" orientation="portrait"><graphic position="anchor" mimetype="image" xlink:href="ark:/27927/pgh113018f2" orientation="portrait" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /></boxed-text></p> </abstract>