<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0185-1101</journal-id>
<journal-title><![CDATA[Revista mexicana de astronomía y astrofísica]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. astron. astrofis]]></abbrev-journal-title>
<issn>0185-1101</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Instituto de Astronomía]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0185-11012019000200237</article-id>
<article-id pub-id-type="doi">10.22201/ia.01851101p.2019.55.02.12</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Dynamics of clusters of galaxies with extended F(&#967;) gravity]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Bernal]]></surname>
<given-names><![CDATA[Tula]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[López-Corona]]></surname>
<given-names><![CDATA[Oliver]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
<xref ref-type="aff" rid="Aaf"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Mendoza]]></surname>
<given-names><![CDATA[Sergio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma Chapingo  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Nacional Autónoma de México Instituto de Astronomía ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Nacional Autónoma de México Centro de Ciencias de la Complejidad ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2019</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2019</year>
</pub-date>
<volume>55</volume>
<numero>2</numero>
<fpage>237</fpage>
<lpage>254</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0185-11012019000200237&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0185-11012019000200237&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0185-11012019000200237&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT In this article, we present the results of a fourth order perturbation analysis of the metric theory of gravity f(&#967;) = &#967;  3/2 , with &#967; a suitable dimensionless Ricci scalar. Such a model corresponds to a specific f(R) metric theory of gravity, where the mass of the system is included in the gravitational field&#8217;s action. In previous works we have shown that, up to the second order in perturbations, this theory reproduces the flat rotation curves of galaxies and the details of the gravitational lensing in individual, groups, and clusters of galaxies. Here, leaving fixed the results from our previous works, we show that the theory reproduces the dynamical masses of 12 Chandra X-ray galaxy clusters, without the need of dark matter, through the metric coefficients up to the fourth order of approximation. In this sense, we calculate the first relativistic correction of the f(&#967;) metric theory and apply it to fit the dynamical masses of clusters of galaxies.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN En este artículo presentamos los resultados del análisis de perturbaciones al cuarto orden de la teoría métrica de gravedad f(&#967;) = &#967;  3/2 , donde &#967; es un escalar de Ricci adimensional. Dicho modelo corresponde a una teoría métrica f(R) en la que la masa del sistema está incluida en la acción del campo gravitacional. En trabajos previos hemos mostrado que, hasta el segundo orden de perturbaciones, la teoría reproduce las curvas de rotación planas de galaxias y los detalles de lentes gravitacionales en galaxias, grupos y cúmulos de galaxias. Aquí, dejando fijos los resultados de nuestros trabajos anteriores, mostramos que la teoría reproduce las masas dinámicas de 12 cúmulos de galaxias del Observatorio Chandra de rayos X, sin materia oscura, a partir de los coeficientes métricos al cuarto orden de aproximación. En este sentido, calculamos la primera corrección relativista de la teoría métrica f(&#967;) y la aplicamos para ajustar las masas dinámicas de los cúmulos de galaxias.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[dark matter]]></kwd>
<kwd lng="en"><![CDATA[gravitation]]></kwd>
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<source><![CDATA[ApJ]]></source>
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